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15. Probability
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  • Question 1/182
    4 / -1
    Mark Review

    A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a = P(X = 3), b = P(X ≥ 3) and c = P(X ≥ 6 ∣ X > 3). Then b + c/a is equal to___

    [27-Jan-2024 Shift 1]

    A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a = P(X = 3), b = P(X ≥ 3) and c = P(X ≥ 6 ∣ X > 3). Then b + c/a is equal to___

    [27-Jan-2024 Shift 1]

  • Question 2/182
    4 / -1
    Mark Review

    An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

    [27-Jan-2024 Shift 2]

    An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

    [27-Jan-2024 Shift 2]

  • Question 3/182
    4 / -1
    Mark Review

    A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

    [29-Jan-2024 Shift 1]

    A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

    [29-Jan-2024 Shift 1]

  • Question 4/182
    4 / -1
    Mark Review

    An integer is chosen at random from the integers 1, 2, 3,...,50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is

    [29-Jan-2024 Shift 2]

    An integer is chosen at random from the integers 1, 2, 3,...,50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is

    [29-Jan-2024 Shift 2]

  • Question 5/182
    4 / -1
    Mark Review

    Two integers x and y are chosen with replacement from the set {0, 1, 2, 3,....,10}. Then the probability that |x − y| > 5 is :

    [30-Jan-2024 Shift 1]

    Two integers x and y are chosen with replacement from the set {0, 1, 2, 3,....,10}. Then the probability that |x − y| > 5 is :

    [30-Jan-2024 Shift 1]

  • Question 6/182
    4 / -1
    Mark Review

    Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn in white, is :

    [30-Jan-2024 Shift 2]

    Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn in white, is :

    [30-Jan-2024 Shift 2]

  • Question 7/182
    4 / -1
    Mark Review

    Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

    [31-Jan-2024 Shift 1]

    Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

    [31-Jan-2024 Shift 1]

  • Question 8/182
    4 / -1
    Mark Review

    Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

    [31-Jan-2024 Shift 1]

    Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

    [31-Jan-2024 Shift 1]

  • Question 9/182
    4 / -1
    Mark Review

    A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

    [31-Jan-2024 Shift 2]

    A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

    [31-Jan-2024 Shift 2]

  • Question 10/182
    4 / -1
    Mark Review

    A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

    [1-Feb-2024 Shift 1]

    A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

    [1-Feb-2024 Shift 1]

  • Question 11/182
    4 / -1
    Mark Review

    Let Ajay will not appear in JEE exam with probability p = 2/7, while both Ajay and Vijay will appear in the exam with probability q = 1/5. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

    [1-Feb-2024 Shift 2]

    Let Ajay will not appear in JEE exam with probability p = 2/7, while both Ajay and Vijay will appear in the exam with probability q = 1/5. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

    [1-Feb-2024 Shift 2]

  • Question 12/182
    4 / -1
    Mark Review
    Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
    x+y+z=1
    2x+Ny+2z=2
    3x+3y+Nz=3
    has unique solution is −, then the sum of value of k and all possible values of N is
    [24-Jan-2023 Shift 1]
    Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
    x+y+z=1
    2x+Ny+2z=2
    3x+3y+Nz=3
    has unique solution is −, then the sum of value of k and all possible values of N is
    [24-Jan-2023 Shift 1]
  • Question 13/182
    4 / -1
    Mark Review
    Let Ω be the sample space and A⊆Ω be an event. Given below are two statements :
    (S1) : If P(A)=0, then A=φ
    (S2) : If P(A)=1, then A=Ω Then
    [24-Jan-2023 Shift 1]
    Let Ω be the sample space and A⊆Ω be an event. Given below are two statements :
    (S1) : If P(A)=0, then A=φ
    (S2) : If P(A)=1, then A=Ω Then
    [24-Jan-2023 Shift 1]
  • Question 14/182
    4 / -1
    Mark Review
    Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S={x∈Z:x(66−x)≥‌
    5
    9
    M    }     and the event A={x∈S:x is a multiple of 3}. Then P(A) is equal to
    [25-Jan-2023 Shift 1]
    Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S={x∈Z:x(66−x)≥‌
    5
    9
    M    }     and the event A={x∈S:x is a multiple of 3}. Then P(A) is equal to
    [25-Jan-2023 Shift 1]
  • Question 15/182
    4 / -1
    Mark Review
    Let x and y be distinct integers where 1≤x≤25 and 1≤y≤25. Then, the number of ways of choosing x and y, such that x+y is divisible by 5 , is _______.
    [25-Jan-2023 Shift 1]
    Let x and y be distinct integers where 1≤x≤25 and 1≤y≤25. Then, the number of ways of choosing x and y, such that x+y is divisible by 5 , is _______.
    [25-Jan-2023 Shift 1]
  • Question 16/182
    4 / -1
    Mark Review
    Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N−2,√3N,N+2 are in geometric progression be ‌
    k
    48
    . Then the value of k is
    [25-Jan-2023 Shift 2]
    Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N−2,√3N,N+2 are in geometric progression be ‌
    k
    48
    . Then the value of k is
    [25-Jan-2023 Shift 2]
  • Question 17/182
    4 / -1
    Mark Review
    25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is ‌
    k
    10
    . Then the value of k is ________.
    [25-Jan-2023 Shift 2]
    25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is ‌
    k
    10
    . Then the value of k is ________.
    [25-Jan-2023 Shift 2]
  • Question 18/182
    4 / -1
    Mark Review
    Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
    [29-Jan-2023 Shift 1]
    Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
    [29-Jan-2023 Shift 1]
  • Question 19/182
    4 / -1
    Mark Review
    Let S={w1,w2,....} be the sample space associated to a random experiment. Let P(wn)=‌
    P(wn−1)
    2
    ,n≥2    .
    Let A={2k+3ℓ;k,ℓ∈ℕ} and B={wn;n∈A}. Then P(B) is equal to
    [29-Jan-2023 Shift 2]
    Let S={w1,w2,....} be the sample space associated to a random experiment. Let P(wn)=‌
    P(wn−1)
    2
    ,n≥2    .
    Let A={2k+3ℓ;k,ℓ∈ℕ} and B={wn;n∈A}. Then P(B) is equal to
    [29-Jan-2023 Shift 2]
  • Question 20/182
    4 / -1
    Mark Review
    If an unbiased die, marked with −2,−1,0,1,2,3 on its faces, is through five times, then the probability that the product of the outcomes is positive, is :
    [30-Jan-2023 Shift 1]
    If an unbiased die, marked with −2,−1,0,1,2,3 on its faces, is through five times, then the probability that the product of the outcomes is positive, is :
    [30-Jan-2023 Shift 1]
  • Question 21/182
    4 / -1
    Mark Review
    A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q. If p:q=m :n, where m and n are coprime, then m+n is equal to _______.
    [30-Jan-2023 Shift 2]
    A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q. If p:q=m :n, where m and n are coprime, then m+n is equal to _______.
    [30-Jan-2023 Shift 2]
  • Question 22/182
    4 / -1
    Mark Review
    A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is
    [31-Jan-2023 Shift 1]
    A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is
    [31-Jan-2023 Shift 1]
  • Question 23/182
    4 / -1
    Mark Review
    Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space [0,60] is less than or equal to a If P(A)=‌
    11
    36
    , then a is equal to _______.
    [31-Jan-2023 Shift 2]
    Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space [0,60] is less than or equal to a If P(A)=‌
    11
    36
    , then a is equal to _______.
    [31-Jan-2023 Shift 2]
  • Question 24/182
    4 / -1
    Mark Review
    In a binomial distribution B(n,p), the sum and product of the mean & variance are 5 and 6 respectively, then find 6(n+p−q) is equal to :-
    [1-Feb-2023 Shift 1]
    In a binomial distribution B(n,p), the sum and product of the mean & variance are 5 and 6 respectively, then find 6(n+p−q) is equal to :-
    [1-Feb-2023 Shift 1]
  • Question 25/182
    4 / -1
    Mark Review
    Two dice are thrown independently. Let A be the event that the number appeared on the 1‌st ‌ die is less than the number appeared on the 2‌nd ‌ die, B be the event that the number appeared on the 1‌st ‌ die is even and that on the second die is odd, and C be the event that the number appeared on the 1‌st ‌ die is odd and that on the 2‌nd ‌ is even. Then
    [1-Feb-2023 Shift 2]
    Two dice are thrown independently. Let A be the event that the number appeared on the 1‌st ‌ die is less than the number appeared on the 2‌nd ‌ die, B be the event that the number appeared on the 1‌st ‌ die is even and that on the second die is odd, and C be the event that the number appeared on the 1‌st ‌ die is odd and that on the 2‌nd ‌ is even. Then
    [1-Feb-2023 Shift 2]
  • Question 26/182
    4 / -1
    Mark Review
    A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If probability of at least 4 successes is ‌
    k
    311
    , then k is equal to :
    [6-Apr-2023 shift 1]
    A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If probability of at least 4 successes is ‌
    k
    311
    , then k is equal to :
    [6-Apr-2023 shift 1]
  • Question 27/182
    4 / -1
    Mark Review
    Three dice are rolled. If the probability of getting different numbers on the three dice is ‌
    p
    q
    , where p and q are co-prime, then q−p is equal to :
    [6-Apr-2023 shift 2]
    Three dice are rolled. If the probability of getting different numbers on the three dice is ‌
    p
    q
    , where p and q are co-prime, then q−p is equal to :
    [6-Apr-2023 shift 2]
  • Question 28/182
    4 / -1
    Mark Review
    In a bolt factory, machines A,B and C manufacture respectively 20%,30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random form the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine C is.
    [8-Apr-2023 shift 1]
    In a bolt factory, machines A,B and C manufacture respectively 20%,30% and 50% of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random form the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine C is.
    [8-Apr-2023 shift 1]
  • Question 29/182
    4 / -1
    Mark Review
    If the probability that the random variable X takes values x is given by P(X=x)=k(x+1)3−x,x=0,1,2,3,..., where k is a constant, then P(X≥2) is equal to
    [8-Apr-2023 shift 2]
    If the probability that the random variable X takes values x is given by P(X=x)=k(x+1)3−x,x=0,1,2,3,..., where k is a constant, then P(X≥2) is equal to
    [8-Apr-2023 shift 2]
  • Question 30/182
    4 / -1
    Mark Review
    Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2N<N ! is ‌
    m
    n
    , where m and n are coprime, then 4m−3n equal to :
    [10-Apr-2023 shift 1]
    Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2N<N ! is ‌
    m
    n
    , where m and n are coprime, then 4m−3n equal to :
    [10-Apr-2023 shift 1]
  • Question 31/182
    4 / -1
    Mark Review
    Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is ‌
    k
    215
    , then k is equal to
    [10-Apr-2023 shift 2]
    Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is ‌
    k
    215
    , then k is equal to
    [10-Apr-2023 shift 2]
  • Question 32/182
    4 / -1
    Mark Review
    Let S={M=[aij],aij∈{0,1,2},1≤i,j≤2} be a sample space and A={M∈S:M is invertible } be an event. Then P(A) is equal to :
    [11-Apr-2023 shift 1]
    Let S={M=[aij],aij∈{0,1,2},1≤i,j≤2} be a sample space and A={M∈S:M is invertible } be an event. Then P(A) is equal to :
    [11-Apr-2023 shift 1]
  • Question 33/182
    4 / -1
    Mark Review
    Let the probability of getting head for a biased coin be ‌
    1
    4
    . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation 64x2+5Nx+1=0 has no real root is ‌
    p
    q
    , where p and q are co-prime, then q−p is equal to _______.
    [11-Apr-2023 shift 2]
    Let the probability of getting head for a biased coin be ‌
    1
    4
    . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation 64x2+5Nx+1=0 has no real root is ‌
    p
    q
    , where p and q are co-prime, then q−p is equal to _______.
    [11-Apr-2023 shift 2]
  • Question 34/182
    4 / -1
    Mark Review
    Two dice A and B are rolled. Let numbers obtained on A and B be α and β respectively. If the variance of α−β is ‌
    p
    q
    , where p and q are co-prime, then the sum of the positive divisior of p is equal to
    [12-Apr-2023 shift 1]
    Two dice A and B are rolled. Let numbers obtained on A and B be α and β respectively. If the variance of α−β is ‌
    p
    q
    , where p and q are co-prime, then the sum of the positive divisior of p is equal to
    [12-Apr-2023 shift 1]
  • Question 35/182
    4 / -1
    Mark Review
    A fair n(n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is ‌
    n
    9
    , then n is equal to _______.
    [12-Apr-2023 shift 1]
    A fair n(n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is ‌
    n
    9
    , then n is equal to _______.
    [12-Apr-2023 shift 1]
  • Question 36/182
    4 / -1
    Mark Review
    A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is-
    [13-Apr-2023 shift 1]
    A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of X is-
    [13-Apr-2023 shift 1]
  • Question 37/182
    4 / -1
    Mark Review
    The random variable X follows binomial distribution B(n,p), for which the difference of the mean and the variance is 1 . If 2P(x=2)=3P(x=1), then n2P(X>1) is equal to
    [13-Apr-2023 shift 2]
    The random variable X follows binomial distribution B(n,p), for which the difference of the mean and the variance is 1 . If 2P(x=2)=3P(x=1), then n2P(X>1) is equal to
    [13-Apr-2023 shift 2]
  • Question 38/182
    4 / -1
    Mark Review
    A bag contains 6 white and 4 black balls. A die is rolled once and the number of ball equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is
    [15-Apr-2023 shift 1]
    A bag contains 6 white and 4 black balls. A die is rolled once and the number of ball equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is
    [15-Apr-2023 shift 1]
  • Question 39/182
    4 / -1
    Mark Review
    A random variable X has the following probability distribution:

    The value of P(1<X<4∣X<2) is equal to:
    [24-Jun-2022-Shift-2]
    A random variable X has the following probability distribution:

    The value of P(1<X<4∣X<2) is equal to:
    [24-Jun-2022-Shift-2]
  • Question 40/182
    4 / -1
    Mark Review
    In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability ‌
    3
    4
     and the remaining 6 questions correctly with probability ‌
    1
    4
    . If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is ‌
    27k
    410
    , then k is equal to __
    [24-Jun-2022-Shift-2]
    In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability ‌
    3
    4
     and the remaining 6 questions correctly with probability ‌
    1
    4
    . If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is ‌
    27k
    410
    , then k is equal to __
    [24-Jun-2022-Shift-2]
  • Question 41/182
    4 / -1
    Mark Review
    Let E1 and E2 be two events such that the conditional probabilities P(E1∣E2)=‌
    1
    2
    ,P(E2∣E1)=‌
    3
    4
     and P(E1∩E2)=‌
    1
    8
    . Then :
    [25-Jun-2022-Shift-1]
    Let E1 and E2 be two events such that the conditional probabilities P(E1∣E2)=‌
    1
    2
    ,P(E2∣E1)=‌
    3
    4
     and P(E1∩E2)=‌
    1
    8
    . Then :
    [25-Jun-2022-Shift-1]
  • Question 42/182
    4 / -1
    Mark Review
    A biased die is marked with numbers 2,4,8,16,32,32 on its faces and the probability of getting a face with mark n is ‌
    1
    n
    . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 , is :
    [25-Jun-2022-Shift-2]
    A biased die is marked with numbers 2,4,8,16,32,32 on its faces and the probability of getting a face with mark n is ‌
    1
    n
    . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 , is :
    [25-Jun-2022-Shift-2]
  • Question 43/182
    4 / -1
    Mark Review
    Five numbers x1,x2,x3,x4,x5 are randomly selected from the numbers 1,2,3,.......,18 and are arranged in the increasing order (x1<x2<x3<x4<x5). The probability that x2=7 and x4=11 is :
    [27-Jun-2022-Shift-1]
    Five numbers x1,x2,x3,x4,x5 are randomly selected from the numbers 1,2,3,.......,18 and are arranged in the increasing order (x1<x2<x3<x4<x5). The probability that x2=7 and x4=11 is :
    [27-Jun-2022-Shift-1]
  • Question 44/182
    4 / -1
    Mark Review
    Let X be a random variable having binomial distribution B(7,p). If P(X=3)=5P(x=4), then the sum of the mean and the variance of X is :
    [27-Jun-2022-Shift-1]
    Let X be a random variable having binomial distribution B(7,p). If P(X=3)=5P(x=4), then the sum of the mean and the variance of X is :
    [27-Jun-2022-Shift-1]
  • Question 45/182
    4 / -1
    Mark Review
    If a point A(x,y) lies in the region bounded by the y-axis, straight lines 2y+x=6 and 5x−6y=30, then the probability that y<1 is
    [27-Jun-2022-Shift-2]
    If a point A(x,y) lies in the region bounded by the y-axis, straight lines 2y+x=6 and 5x−6y=30, then the probability that y<1 is
    [27-Jun-2022-Shift-2]
  • Question 46/182
    4 / -1
    Mark Review
    Let S={E1,E2,.........,E8} be a sample space of a random experiment such that P(En)=‌
    n
    36
     for every n=1,2,...
    8. Then the number of elements in the set {A⊆S:P(A)≥‌
    4
    5
    }     is___
    [27-Jun-2022-Shift-2]
    Let S={E1,E2,.........,E8} be a sample space of a random experiment such that P(En)=‌
    n
    36
     for every n=1,2,...
    8. Then the number of elements in the set {A⊆S:P(A)≥‌
    4
    5
    }     is___
    [27-Jun-2022-Shift-2]
  • Question 47/182
    4 / -1
    Mark Review
    The probability, that in a randomly selected 3-digit number at least two digits are odd, is
    [28-Jun-2022-Shift-1]
    The probability, that in a randomly selected 3-digit number at least two digits are odd, is
    [28-Jun-2022-Shift-1]
  • Question 48/182
    4 / -1
    Mark Review
    Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is ‌
    6
    11
    , then n is equal to
    [24-Jun-2022-Shift-1]
    Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is ‌
    6
    11
    , then n is equal to
    [24-Jun-2022-Shift-1]
  • Question 49/182
    4 / -1
    Mark Review
    If a random variable X follows the Binomial distribution B(33,p) such that 3P(X=0)=P(X=1), then the value of ‌
    P(X=15)
    P(X=18)
    −‌
    P(X=16)
    P(X=17)
     is equal to:
    [24-Jun-2022-Shift-1]
    If a random variable X follows the Binomial distribution B(33,p) such that 3P(X=0)=P(X=1), then the value of ‌
    P(X=15)
    P(X=18)
    −‌
    P(X=16)
    P(X=17)
     is equal to:
    [24-Jun-2022-Shift-1]
  • Question 50/182
    4 / -1
    Mark Review
    If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is:
    [25-Jul-2022-Shift-1]
    If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is:
    [25-Jul-2022-Shift-1]
  • Question 51/182
    4 / -1
    Mark Review
    If A and B are two events such that P(A)=‌
    1
    3
    ,P(B)=‌
    1
    5
     and P(A∪B)=‌
    1
    2
    , then P(A∣B′)+P(B∣A′) is equal to
    [25-Jul-2022-Shift-2]
    If A and B are two events such that P(A)=‌
    1
    3
    ,P(B)=‌
    1
    5
     and P(A∪B)=‌
    1
    2
    , then P(A∣B′)+P(B∣A′) is equal to
    [25-Jul-2022-Shift-2]
  • Question 52/182
    4 / -1
    Mark Review
    The mean and variance of a binomial distribution are α and ‌
    α
    3
     respectively. If P(X=1)=‌
    4
    243
    , then P(X=4 or 5) is equal to :
    [26-Jul-2022-Shift-1]
    The mean and variance of a binomial distribution are α and ‌
    α
    3
     respectively. If P(X=1)=‌
    4
    243
    , then P(X=4 or 5) is equal to :
    [26-Jul-2022-Shift-1]
  • Question 53/182
    4 / -1
    Mark Review
    Let E1,E2,E3 be three mutually exclusive events such that P(E1)=‌
    2+3p
    6
    ,P(E2)=‌
    2−p
    8
     and P(E3)=‌
    1−p
    2
    . If the maximum and minimum values of p are p1 and p2, then (p1+p2) is equal to
    [26-Jul-2022-Shift-1]
    Let E1,E2,E3 be three mutually exclusive events such that P(E1)=‌
    2+3p
    6
    ,P(E2)=‌
    2−p
    8
     and P(E3)=‌
    1−p
    2
    . If the maximum and minimum values of p are p1 and p2, then (p1+p2) is equal to
    [26-Jul-2022-Shift-1]
  • Question 54/182
    4 / -1
    Mark Review
    Let X be a binomially distributed random variable with mean 4 and variance ‌
    4
    3
    . Then, 54P(X≤2) is equal to
    [26-Jul-2022-Shift-2]
    Let X be a binomially distributed random variable with mean 4 and variance ‌
    4
    3
    . Then, 54P(X≤2) is equal to
    [26-Jul-2022-Shift-2]
  • Question 55/182
    4 / -1
    Mark Review
    Let X have a binomial distribution B(n,p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If P(X>n−3)=‌
    k
    2n
    , then k is equal to :
    [27-Jul-2022-Shift-2]
    Let X have a binomial distribution B(n,p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If P(X>n−3)=‌
    k
    2n
    , then k is equal to :
    [27-Jul-2022-Shift-2]
  • Question 56/182
    4 / -1
    Mark Review
    A six faced die is biased such that
    3×P( a prime number )=6×P( a composite number )=2×P.
    Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :
    [27-Jul-2022-Shift-2]
    A six faced die is biased such that
    3×P( a prime number )=6×P( a composite number )=2×P.
    Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :
    [27-Jul-2022-Shift-2]
  • Question 57/182
    4 / -1
    Mark Review
    Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :
    [28-Jul-2022-Shift-1]
    Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :
    [28-Jul-2022-Shift-1]
  • Question 58/182
    4 / -1
    Mark Review
    Let A and B be two events such that P(B∣A)=‌
    2
    5
    ,P(A∣B)=‌
    1
    7
     and P(A∩B)=‌
    1
    9
    ⋅     Consider
    (S1) P(A′∪B)=‌
    5
    6
    ,
    (S2) P(A′∩B′)=‌
    1
    18

    Then
    [28-Jul-2022-Shift-2]
    Let A and B be two events such that P(B∣A)=‌
    2
    5
    ,P(A∣B)=‌
    1
    7
     and P(A∩B)=‌
    1
    9
    ⋅     Consider
    (S1) P(A′∪B)=‌
    5
    6
    ,
    (S2) P(A′∩B′)=‌
    1
    18

    Then
    [28-Jul-2022-Shift-2]
  • Question 59/182
    4 / -1
    Mark Review
    A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ2 is the variance of X, then 100σ2 is equal to_______.
    [28-Jul-2022-Shift-2]
    A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ2 is the variance of X, then 100σ2 is equal to_______.
    [28-Jul-2022-Shift-2]
  • Question 60/182
    4 / -1
    Mark Review
    Let S={1,2,3,...,2022}. Then the probability, that a randomly chosen number n from the set S such that HCF(n,2022)=1, is :
    [29-Jul-2022-Shift-1]
    Let S={1,2,3,...,2022}. Then the probability, that a randomly chosen number n from the set S such that HCF(n,2022)=1, is :
    [29-Jul-2022-Shift-1]
  • Question 61/182
    4 / -1
    Mark Review
    Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:
    [29-Jul-2022-Shift-2]
    Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:
    [29-Jul-2022-Shift-2]
  • Question 62/182
    4 / -1
    Mark Review
    The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _______.
    [29-Jul-2022-Shift-2]
    The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _______.
    [29-Jul-2022-Shift-2]
  • Question 63/182
    4 / -1
    Mark Review
    A seven digit number is formed using digits 3,3,4,4,4,5,5. The probability, that number so formed is divisible by 2 , is
    [2021, 26 Feb. Shift-II]
    A seven digit number is formed using digits 3,3,4,4,4,5,5. The probability, that number so formed is divisible by 2 , is
    [2021, 26 Feb. Shift-II]
  • Question 64/182
    4 / -1
    Mark Review
    In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%,20% and 10%, respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is
    [2021, 25 Feb. Shift-II]
    In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%,20% and 10%, respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is
    [2021, 25 Feb. Shift-II]
  • Question 65/182
    4 / -1
    Mark Review
    Let Bi(i=1,2,3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let P be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α−2β)P=αβ and (β−3γ)P=2βγ( All the probabilities are assumed to lie in the interval (0,1)). Then, ‌
    P(B1)
    P(B3)
     is equal to .......
    [2021, 24 Feb. Shift-l]
    Let Bi(i=1,2,3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let P be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α−2β)P=αβ and (β−3γ)P=2βγ( All the probabilities are assumed to lie in the interval (0,1)). Then, ‌
    P(B1)
    P(B3)
     is equal to .......
    [2021, 24 Feb. Shift-l]
  • Question 66/182
    4 / -1
    Mark Review
    When a missile is fired from a ship, the probability that it is intercepted is ‌
    1
    3
     and the probability that the missile hits the target, given that it is not intercepted, is ‌
    3
    4
    . If three missiles are fired independently from the ship, then the probability that all three hit the target, is
    [2021, 25 Feb. Shift-1]
    When a missile is fired from a ship, the probability that it is intercepted is ‌
    1
    3
     and the probability that the missile hits the target, given that it is not intercepted, is ‌
    3
    4
    . If three missiles are fired independently from the ship, then the probability that all three hit the target, is
    [2021, 25 Feb. Shift-1]
  • Question 67/182
    4 / -1
    Mark Review
    An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :
    24 Feb 2021 Shift 1
    An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :
    24 Feb 2021 Shift 1
  • Question 68/182
    4 / -1
    Mark Review
    Let Bi(i=1,2,3) be three independent events in a sample space. The probability that only B1 occur is α. Only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α−2β)p=αβ and (β−3γ)p=2βγ (All the probabilities are assumed to lie in the interval (0,1) ). Then ‌
    P(B1)
    P(B3)
     is equal to
    24 Feb 2021 Shift 1
    Let Bi(i=1,2,3) be three independent events in a sample space. The probability that only B1 occur is α. Only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α−2β)p=αβ and (β−3γ)p=2βγ (All the probabilities are assumed to lie in the interval (0,1) ). Then ‌
    P(B1)
    P(B3)
     is equal to
    24 Feb 2021 Shift 1
  • Question 69/182
    4 / -1
    Mark Review
    Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then, the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is
    [2021, 25 Feb. Shift-11]
    Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then, the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is
    [2021, 25 Feb. Shift-11]
  • Question 70/182
    4 / -1
    Mark Review
    The coefficients a,b and c of the quadratic equation, ax2+bx+c=0 are obtained by throwing a dice three times. The probability that this equation has equal roots is
    [2021, 25 Feb. Shift-1]
    The coefficients a,b and c of the quadratic equation, ax2+bx+c=0 are obtained by throwing a dice three times. The probability that this equation has equal roots is
    [2021, 25 Feb. Shift-1]
  • Question 71/182
    4 / -1
    Mark Review
    The probability that two randomly selected subsets of the set {1,2,3, 4,5} have exactly two elements in their intersection, is
    [2021, 24 Feb. Shift-II]
    The probability that two randomly selected subsets of the set {1,2,3, 4,5} have exactly two elements in their intersection, is
    [2021, 24 Feb. Shift-II]
  • Question 72/182
    4 / -1
    Mark Review
    Two dices are rolle(d) If both dices have six faces numbered 1,2,3,5,7 and 11 , then the probability that the sum of the numbers on the top faces is less than or equal to 8 is
    [2021, 17 March Shift-1]
    Two dices are rolle(d) If both dices have six faces numbered 1,2,3,5,7 and 11 , then the probability that the sum of the numbers on the top faces is less than or equal to 8 is
    [2021, 17 March Shift-1]
  • Question 73/182
    4 / -1
    Mark Review
    Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be ‌
    1
    2
     and probability of occurrence of 0 at the odd place be ‌
    1
    3
    . Then, the probability that '10' is followed by ' 01′ is equal to
    [2021, 17 March Shift-II]
    Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be ‌
    1
    2
     and probability of occurrence of 0 at the odd place be ‌
    1
    3
    . Then, the probability that '10' is followed by ' 01′ is equal to
    [2021, 17 March Shift-II]
  • Question 74/182
    4 / -1
    Mark Review
    Let A denote the event that a 6 -digit integer formed by 0,1,2,3, 4,5,6 without repetitions, be divisible by 3 . Then, probability of event A is equal to
    [2021, 16 March Shift-II]
    Let A denote the event that a 6 -digit integer formed by 0,1,2,3, 4,5,6 without repetitions, be divisible by 3 . Then, probability of event A is equal to
    [2021, 16 March Shift-II]
  • Question 75/182
    4 / -1
    Mark Review
    A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is
    [2021, 16 March Shift-1]
    A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is
    [2021, 16 March Shift-1]
  • Question 76/182
    4 / -1
    Mark Review
    Let there be three independent events E1,E2 and E3. The probability that only E1 occurs is α, only E2 occurs is β and only E3 occurs is γ. Let p denote the probability of none of events occur that satisfies the equations (α−2β)p=αβ and (β−3γ)p=2βγ. All the given probabilities are assumed to lie in the interval (0,1). Then, probability of occurrence of E1 probability of occurrence of E3 is equal to ..........
    [2021, 17 March Shift-1]
    Let there be three independent events E1,E2 and E3. The probability that only E1 occurs is α, only E2 occurs is β and only E3 occurs is γ. Let p denote the probability of none of events occur that satisfies the equations (α−2β)p=αβ and (β−3γ)p=2βγ. All the given probabilities are assumed to lie in the interval (0,1). Then, probability of occurrence of E1 probability of occurrence of E3 is equal to ..........
    [2021, 17 March Shift-1]
  • Question 77/182
    4 / -1
    Mark Review
    Let 9 distinct balls be distributed among 4 boxes, B1,B2,B3 and B4. If the probability that B3 contains exactly 3 balls is k(‌
    3
    4
    )    9    , then k lies in the set
    [2021, 25 July Shift-1]
    Let 9 distinct balls be distributed among 4 boxes, B1,B2,B3 and B4. If the probability that B3 contains exactly 3 balls is k(‌
    3
    4
    )    9    , then k lies in the set
    [2021, 25 July Shift-1]
  • Question 78/182
    4 / -1
    Mark Review
    The probability that a randomly selected 2-digit number belongs to the set {n∈N:(2n−2) is a multiple of 3} is equal to
    [2021, 27 July Shift-1]
    The probability that a randomly selected 2-digit number belongs to the set {n∈N:(2n−2) is a multiple of 3} is equal to
    [2021, 27 July Shift-1]
  • Question 79/182
    4 / -1
    Mark Review
    The probability of selecting integers a∈[−5,30] such that x2+2(a+4)x−5a+64>0, for all x∈R, is
    [2021, 20 July Shift-1]
    The probability of selecting integers a∈[−5,30] such that x2+2(a+4)x−5a+64>0, for all x∈R, is
    [2021, 20 July Shift-1]
  • Question 80/182
    4 / -1
    Mark Review
    Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2×2 matrices. The probability that such formed matrices have all different entries and are non singular, is
    [2021, 22 July Shift-II]
    Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2×2 matrices. The probability that such formed matrices have all different entries and are non singular, is
    [2021, 22 July Shift-II]
  • Question 81/182
    4 / -1
    Mark Review
    Let A,B and C be three events such that the probability that exactly one of A and B occurs is (1−k), the probability that exactly one of B and C occurs is (1−2k), the probability that exactly one of C and A occurs is (1−k) and the probability of all A,B and C occur simultaneously is k2, where 0<k<1. Then the probability that at least one of A,B and C occur is
    [2021, 20 July Shift-II]
    Let A,B and C be three events such that the probability that exactly one of A and B occurs is (1−k), the probability that exactly one of B and C occurs is (1−2k), the probability that exactly one of C and A occurs is (1−k) and the probability of all A,B and C occur simultaneously is k2, where 0<k<1. Then the probability that at least one of A,B and C occur is
    [2021, 20 July Shift-II]
  • Question 82/182
    4 / -1
    Mark Review
    Let S={1,2,3,4,5,6}. Then, the probability that a randomly chosen onto function g from S to S satisfies g(3)=2g(1) is
    [2021, 31 Aug. Shift-II]
    Let S={1,2,3,4,5,6}. Then, the probability that a randomly chosen onto function g from S to S satisfies g(3)=2g(1) is
    [2021, 31 Aug. Shift-II]
  • Question 83/182
    4 / -1
    Mark Review
    When a certain biased die is rolled, a particular face occurs with probability ‌
    1
    6
    −x     and its opposite face occurs with probability ‌
    1
    6
    +x    .
    All other faces occur with probability 1∕6. Note that opposite faces sum to 7 in any die. If 0<x<‌
    1
    6
    , and the probability of obtaining total sum =7, when such a die is rolled twice is 13∕96, then the value of x is
    [2021, 27 Aug. Shift-1]
    When a certain biased die is rolled, a particular face occurs with probability ‌
    1
    6
    −x     and its opposite face occurs with probability ‌
    1
    6
    +x    .
    All other faces occur with probability 1∕6. Note that opposite faces sum to 7 in any die. If 0<x<‌
    1
    6
    , and the probability of obtaining total sum =7, when such a die is rolled twice is 13∕96, then the value of x is
    [2021, 27 Aug. Shift-1]
  • Question 84/182
    4 / -1
    Mark Review
    An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is P, then 98P is equal to
    [2021, 31 Aug. Shift-1]
    An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is P, then 98P is equal to
    [2021, 31 Aug. Shift-1]
  • Question 85/182
    4 / -1
    Mark Review
    Let A and B be independent events such that P(A)=p and P(B)=2p. The largest value of p, for which P (exactly one of A,B occurs) =‌
    5
    9
    , is
    [2021, 26 Aug. Shift-1]
    Let A and B be independent events such that P(A)=p and P(B)=2p. The largest value of p, for which P (exactly one of A,B occurs) =‌
    5
    9
    , is
    [2021, 26 Aug. Shift-1]
  • Question 86/182
    4 / -1
    Mark Review
    A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X≥5∣X>2) is
    [2021, 26 Aug. Shift-II]
    A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X≥5∣X>2) is
    [2021, 26 Aug. Shift-II]
  • Question 87/182
    4 / -1
    Mark Review
    Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is

    [2021, 01 Sep. Shift-II]
    Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is

    [2021, 01 Sep. Shift-II]
  • Question 88/182
    4 / -1
    Mark Review
    In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is:
    [Jan. 9,2020 (I)]
    In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is:
    [Jan. 9,2020 (I)]
  • Question 89/182
    4 / -1
    Mark Review
    Let A and B be two independent events such thatP(A)=
    1
    3
     and P(B)=
    1
    6
    .     Then, which of the following is TRUE?
    [Jan. 8, 2020 (I)]
    Let A and B be two independent events such thatP(A)=
    1
    3
     and P(B)=
    1
    6
    .     Then, which of the following is TRUE?
    [Jan. 8, 2020 (I)]
  • Question 90/182
    4 / -1
    Mark Review
    An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k=3,4,5, otherwise X takes the value -1 . Then the expected value of X, is:
    [Jan. 7, 2020 (I)]
    An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k=3,4,5, otherwise X takes the value -1 . Then the expected value of X, is:
    [Jan. 7, 2020 (I)]
  • Question 91/182
    4 / -1
    Mark Review
    In a workshop, there are five machines and the probability of any one of them to be out of service on a day is
    1
    4
    . If the probability that at most two machines will be out of service on the same day is (
    3
    4
    )    3    k    ,     then k is equal to:
    [Jan. 7,2020 (II)]
    In a workshop, there are five machines and the probability of any one of them to be out of service on a day is
    1
    4
    . If the probability that at most two machines will be out of service on the same day is (
    3
    4
    )    3    k    ,     then k is equal to:
    [Jan. 7,2020 (II)]
  • Question 92/182
    4 / -1
    Mark Review
    Let A and B be two events such that the probability that exactly one of them occurs is
    2
    5
     and the probability thatA or B occurs is
    1
    2
    ,     then the probability of both of them occur together is:
    [Jan. 8, 2020 (II)]
    Let A and B be two events such that the probability that exactly one of them occurs is
    2
    5
     and the probability thatA or B occurs is
    1
    2
    ,     then the probability of both of them occur together is:
    [Jan. 8, 2020 (II)]
  • Question 93/182
    4 / -1
    Mark Review
    If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
    [Jan. 9, 2020 (II)]
    If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :
    [Jan. 9, 2020 (II)]
  • Question 94/182
    4 / -1
    Mark Review
    A random variable X has the following probability distribution:
    Then, P(X > 2) is equal to:
    [Jan. 9, 2020 (II)]
    A random variable X has the following probability distribution:

    Then, P(X > 2) is equal to:
    [Jan. 9, 2020 (II)]
  • Question 95/182
    4 / -1
    Mark Review
    In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins.
    The probability of A winning the game is :
    [Sep. 04, 2020 (II)]
    In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins.
    The probability of A winning the game is :
    [Sep. 04, 2020 (II)]
  • Question 96/182
    4 / -1
    Mark Review
    A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
    [Sep. 03, 2020 (I)]
    A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
    [Sep. 03, 2020 (I)]
  • Question 97/182
    4 / -1
    Mark Review
    The probability that a randomly chosen 5 -digit number is made from exactly two digits is:
    [Sep. 03, 2020 (II)]
    The probability that a randomly chosen 5 -digit number is made from exactly two digits is:
    [Sep. 03, 2020 (II)]
  • Question 98/182
    4 / -1
    Mark Review
    Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :
    [Sep. 02, 2020 (I)]
    Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :
    [Sep. 02, 2020 (I)]
  • Question 99/182
    4 / -1
    Mark Review
    Let EC denote the complement of an event E. Let E1,E2 and E3 be any pairwise independent events with P(E1)>0
    and P(E1∩E2∩E3)=0
    Then P(E2C∩E3C∕E1) is equal to:
    [Sep. 02, 2020 (II)]
    Let EC denote the complement of an event E. Let E1,E2 and E3 be any pairwise independent events with P(E1)>0
    and P(E1∩E2∩E3)=0
    Then P(E2C∩E3C∕E1) is equal to:
    [Sep. 02, 2020 (II)]
  • Question 100/182
    4 / -1
    Mark Review
    Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.
    [NA Sep. 05, 2020 (I)]
    Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.
    [NA Sep. 05, 2020 (I)]
  • Question 101/182
    4 / -1
    Mark Review
    In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is _________.
    [NA Sep. 05, 2020 (II)]
    In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is _________.
    [NA Sep. 05, 2020 (II)]
  • Question 102/182
    4 / -1
    Mark Review
    The probability of a man hitting a target is
    1
    10
    .     The least number of shots required, so that the probability of his hitting the target at least once is greater than
    1
    4
    , is ________.
    [NA Sep. 04, 2020 (I)]
    The probability of a man hitting a target is
    1
    10
    .     The least number of shots required, so that the probability of his hitting the target at least once is greater than
    1
    4
    , is ________.
    [NA Sep. 04, 2020 (I)]
  • Question 103/182
    4 / -1
    Mark Review
    Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
    [Sep. 06, 2020 (I)]
    Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
    [Sep. 06, 2020 (I)]
  • Question 104/182
    4 / -1
    Mark Review
    The probabilities of three events A,B and C are given by P(A)=0.6,P(B)=0.4 and P(C)=0.5. If P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2,P(B∩C)=βP(A∪B∪C)=α, where 0.85≤α≤0.95, then β lies in the interval:
    [Sep. 06, 2020 (II)]
    The probabilities of three events A,B and C are given by P(A)=0.6,P(B)=0.4 and P(C)=0.5. If P(A∪B)=0.8,P(A∩C)=0.3,P(A∩B∩C)=0.2,P(B∩C)=βP(A∪B∪C)=α, where 0.85≤α≤0.95, then β lies in the interval:
    [Sep. 06, 2020 (II)]
  • Question 105/182
    4 / -1
    Mark Review
    Let S = {1, 2, ....., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Than the probability that a randomly chosen subset of S is “nice” is :
    [Jan. 11, 2019 (II)]
    Let S = {1, 2, ....., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Than the probability that a randomly chosen subset of S is “nice” is :
    [Jan. 11, 2019 (II)]
  • Question 106/182
    4 / -1
    Mark Review
    In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
    [Jan. 12, 2019 (II)]
    In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
    [Jan. 12, 2019 (II)]
  • Question 107/182
    4 / -1
    Mark Review
    In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:
    [Jan. 12, 2019 (I)]
    In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:
    [Jan. 12, 2019 (I)]
  • Question 108/182
    4 / -1
    Mark Review
    In a game, a man wins Rs.100 if the gets 5 or 6 on a throw of a fair die and loses Rs.50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is:
    [Jan. 12, 2019 (II)]
    In a game, a man wins Rs.100 if the gets 5 or 6 on a throw of a fair die and loses Rs.50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is:
    [Jan. 12, 2019 (II)]
  • Question 109/182
    4 / -1
    Mark Review
    Two integers are selected at random from the set {1,2,....,11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:
    [Jan. 11, 2019 (I)]
    Two integers are selected at random from the set {1,2,....,11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:
    [Jan. 11, 2019 (I)]
  • Question 110/182
    4 / -1
    Mark Review
    An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1,2,3,......,9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is:
    [Jan 10, 2019 (I)]
    An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1,2,3,......,9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is:
    [Jan 10, 2019 (I)]
  • Question 111/182
    4 / -1
    Mark Review
    If the probability of hitting a target by a shooter, in any shot, is
    1
    3
    ,     then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than
    5
    6
    , is:
    [Jan. 10, 2019 (II)]
    If the probability of hitting a target by a shooter, in any shot, is
    1
    3
    ,     then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than
    5
    6
    , is:
    [Jan. 10, 2019 (II)]
  • Question 112/182
    4 / -1
    Mark Review
    Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals:
    [Jan 09, 2019 (I)]
    Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals:
    [Jan 09, 2019 (I)]
  • Question 113/182
    4 / -1
    Mark Review
    An urn contains 5 red and 2 green balls. Aball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is:
    [Jan. 09, 2019 (II)]
    An urn contains 5 red and 2 green balls. Aball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is:
    [Jan. 09, 2019 (II)]
  • Question 114/182
    4 / -1
    Mark Review
    A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then(
    mean of X
    standard deviation of X
    )     is equal to:
    [Jan. 11, 2019 (II)]
    A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then(
    mean of X
    standard deviation of X
    )     is equal to:
    [Jan. 11, 2019 (II)]
  • Question 115/182
    4 / -1
    Mark Review
    Let A and B be two non-null events such that A⊂B. Then, which of the following statements is always correct?
    [April 08, 2019 (I)]
    Let A and B be two non-null events such that A⊂B. Then, which of the following statements is always correct?
    [April 08, 2019 (I)]
  • Question 116/182
    4 / -1
    Mark Review
    The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :
    [April. 08, 2019 (II)]
    The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :
    [April. 08, 2019 (II)]
  • Question 117/182
    4 / -1
    Mark Review
    Four persons can hit a target correctly with probabilities
    1
    2
    ,
    1
    3
    ,
    1
    4
     and
    1
    8
     respectively. If all hit at the target independently, then the probability that the target would be hit, is:
    [April 09, 2019 (I)]
    Four persons can hit a target correctly with probabilities
    1
    2
    ,
    1
    3
    ,
    1
    4
     and
    1
    8
     respectively. If all hit at the target independently, then the probability that the target would be hit, is:
    [April 09, 2019 (I)]
  • Question 118/182
    4 / -1
    Mark Review
    Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:
    [April 10, 2019 (I)]
    Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:
    [April 10, 2019 (I)]
  • Question 119/182
    4 / -1
    Mark Review
    Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :
    [April 10, 2019 (II)]
    Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :
    [April 10, 2019 (II)]
  • Question 120/182
    4 / -1
    Mark Review
    If three of the six vertices of a regular hexazon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :
    [April 12, 2019 (I)]
    If three of the six vertices of a regular hexazon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :
    [April 12, 2019 (I)]
  • Question 121/182
    4 / -1
    Mark Review
    For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is
    4
    5
    ,     then the probability that he is unable to solve less than two problems is:
    [April 12, 2019(II)]
    For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is
    4
    5
    ,     then the probability that he is unable to solve less than two problems is:
    [April 12, 2019(II)]
  • Question 122/182
    4 / -1
    Mark Review
    Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(Xd"2)=
    k
    216
    ,     then k is equal to:
    [April 12, 2019 (I)]
    Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(Xd"2)=
    k
    216
    ,     then k is equal to:
    [April 12, 2019 (I)]
  • Question 123/182
    4 / -1
    Mark Review
    A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
    [April 12, 2019 (II)]
    A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
    [April 12, 2019 (II)]
  • Question 124/182
    4 / -1
    Mark Review
    Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket.
    If the probability that all the tickets go to the children ofthe family B is
    1
    12
     , then the number of children in each family is?
    [Online April 16, 2018]
    Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket.
    If the probability that all the tickets go to the children ofthe family B is
    1
    12
     , then the number of children in each family is?
    [Online April 16, 2018]
  • Question 125/182
    4 / -1
    Mark Review
    A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is
    [Online April 15, 2018]
    A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is
    [Online April 15, 2018]
  • Question 126/182
    4 / -1
    Mark Review
    A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :
    [2018]
    A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :
    [2018]
  • Question 127/182
    4 / -1
    Mark Review
    Let A,B and C be three events, which are pair-wise independence and E denotes the complement of an event E. If P(A∩B∩C)=0 and P(C)>0, then P[(A∩B)|C] is equal to.
    [Online April 16, 2018]
    Let A,B and C be three events, which are pair-wise independence and E denotes the complement of an event E. If P(A∩B∩C)=0 and P(C)>0, then P[(A∩B)|C] is equal to.
    [Online April 16, 2018]
  • Question 128/182
    4 / -1
    Mark Review
    A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' p ' is
    [Online April 15, 2018]
    A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' p ' is
    [Online April 15, 2018]
  • Question 129/182
    4 / -1
    Mark Review
    For three events A, B and C,
    P(Exactly one of A or B occurs)
    = P(Exactly one of B or C occurs)
    = P(Exactly one of C or A occurs) =
    1
    4
     and
    P(All the three events occur simultaneously) =
    1
    16
    .
    Then the probability that at least one of the events occurs, is :
    [2017]
    For three events A, B and C,
    P(Exactly one of A or B occurs)
    = P(Exactly one of B or C occurs)
    = P(Exactly one of C or A occurs) =
    1
    4
     and
    P(All the three events occur simultaneously) =
    1
    16
    .
    Then the probability that at least one of the events occurs, is :
    [2017]
  • Question 130/182
    4 / -1
    Mark Review
    From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
    [Online April 9, 2017]
    From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
    [Online April 9, 2017]
  • Question 131/182
    4 / -1
    Mark Review
    If two different numbers are taken from the set (0,1,2,3, ......,10 ), then the probability that their sum as well as absolute difference are both multiple of 4, is :
    [2017]
    If two different numbers are taken from the set (0,1,2,3, ......,10 ), then the probability that their sum as well as absolute difference are both multiple of 4, is :
    [2017]
  • Question 132/182
    4 / -1
    Mark Review
    Let E and F be two independent events. The probability that both E and F happen is
    1
    12
     and the probability that neither E nor F happens is
    1
    2
    ,     then a value of
    P(E)
    P(F)
     is
    [Online April 9, 2017]
    Let E and F be two independent events. The probability that both E and F happen is
    1
    12
     and the probability that neither E nor F happens is
    1
    2
    ,     then a value of
    P(E)
    P(F)
     is
    [Online April 9, 2017]
  • Question 133/182
    4 / -1
    Mark Review
    Three persons P,Q and R independently try to hit a target. If the probabilities of their hitting the target are
    3
    4
    ,
    1
    2
     and
    5
    8
     respectively, then the probability that the target is hit by P or Q but not by R is :
    [Online April 8, 2017]
    Three persons P,Q and R independently try to hit a target. If the probabilities of their hitting the target are
    3
    4
    ,
    1
    2
     and
    5
    8
     respectively, then the probability that the target is hit by P or Q but not by R is :
    [Online April 8, 2017]
  • Question 134/182
    4 / -1
    Mark Review
    An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:
    [Online April 8, 2017]
    An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:
    [Online April 8, 2017]
  • Question 135/182
    4 / -1
    Mark Review
    A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:
    [2017]
    A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:
    [2017]
  • Question 136/182
    4 / -1
    Mark Review
    Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
    [2016]
    Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
    [2016]
  • Question 137/182
    4 / -1
    Mark Review
    If A and B are any two events such that P(A)=
    2
    5
     andP(A∩B)=
    3
    20
    ,     then the conditional probability,P(A|A′∪B′)), where A′ denotes the complement of A, is equal to :
    [Online April 9, 2016]
    If A and B are any two events such that P(A)=
    2
    5
     andP(A∩B)=
    3
    20
    ,     then the conditional probability,P(A|A′∪B′)), where A′ denotes the complement of A, is equal to :
    [Online April 9, 2016]
  • Question 138/182
    4 / -1
    Mark Review
    An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is:
    [Online April 10, 2016]
    An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is:
    [Online April 10, 2016]
  • Question 139/182
    4 / -1
    Mark Review
    If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :
    [Online April 11, 2015]
    If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :
    [Online April 11, 2015]
  • Question 140/182
    4 / -1
    Mark Review
    If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :
    (2015)
    If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :
    (2015)
  • Question 141/182
    4 / -1
    Mark Review
    Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X) with replacement, then the probability that A and B have equal number elements, is:
    [Online April 10, 2015]
    Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X) with replacement, then the probability that A and B have equal number elements, is:
    [Online April 10, 2015]
  • Question 142/182
    4 / -1
    Mark Review
    If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is:
    [Online April 11, 2015]
    If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is:
    [Online April 11, 2015]
  • Question 143/182
    4 / -1
    Mark Review
    A number x is chosen at random from the set {1,2,3,4,....... 100\} . Define the event: A= the chosen number x satisfies
    (x−10)(x−50)
    (x−30)
    ≥0
    Then P (A) is:
    [Online April 12, 2014]
    A number x is chosen at random from the set {1,2,3,4,....... 100\} . Define the event: A= the chosen number x satisfies
    (x−10)(x−50)
    (x−30)
    ≥0
    Then P (A) is:
    [Online April 12, 2014]
  • Question 144/182
    4 / -1
    Mark Review
    A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x ∈ A is:
    [Online April 11, 2014]
    A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x ∈ A is:
    [Online April 11, 2014]
  • Question 145/182
    4 / -1
    Mark Review
    If A and B are two events such thatP(A∪B)=P(A∩B), then the incorrect statement amongst the following statements is:
    [Online April 9, 2014]
    If A and B are two events such thatP(A∪B)=P(A∩B), then the incorrect statement amongst the following statements is:
    [Online April 9, 2014]
  • Question 146/182
    4 / -1
    Mark Review
    Let A and B be two events such that P(A∪B)=
    1
    6
    , P(A∩B)=
    1
    4
     and P(A)=
    1
    4
    ,     where A stands for the complement of the event A. Then the events A and B are
    [2014]
    Let A and B be two events such that P(A∪B)=
    1
    6
    , P(A∩B)=
    1
    4
     and P(A)=
    1
    4
    ,     where A stands for the complement of the event A. Then the events A and B are
    [2014]
  • Question 147/182
    4 / -1
    Mark Review
    Let A and E be any two events with positive probabilities:
    Statement -1: P(E∕A)≥P(A∕E)P(E)
    Statement -2:P(A∕E)≥P(A∩E)
    [Online April 19, 2014]
    Let A and E be any two events with positive probabilities:
    Statement -1: P(E∕A)≥P(A∕E)P(E)
    Statement -2:P(A∕E)≥P(A∩E)
    [Online April 19, 2014]
  • Question 148/182
    4 / -1
    Mark Review
    If X has a binomial distribution, B(n,p) with parameters n and p such that P(X=2)=P(X=3), then E(X), the mean of variable X, is
    [Online April 11, 2014]
    If X has a binomial distribution, B(n,p) with parameters n and p such that P(X=2)=P(X=3), then E(X), the mean of variable X, is
    [Online April 11, 2014]
  • Question 149/182
    4 / -1
    Mark Review
    If the events A and B are mutually exclusive events such that P(A)=
    3x+1
    3
     and P(B)=
    1−x
    4
    ,     then the set of possible values of x lies in the interval :
    [Online April 25, 2013]
    If the events A and B are mutually exclusive events such that P(A)=
    3x+1
    3
     and P(B)=
    1−x
    4
    ,     then the set of possible values of x lies in the interval :
    [Online April 25, 2013]
  • Question 150/182
    4 / -1
    Mark Review
    A, B, C try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are
    3
    4
    ,
    1
    2
    ,
    5
    8
    .     The probability that the target is hit by A or B but not by C is :
    [Online April 23, 2013]
    A, B, C try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are
    3
    4
    ,
    1
    2
    ,
    5
    8
    .     The probability that the target is hit by A or B but not by C is :
    [Online April 23, 2013]
  • Question 151/182
    4 / -1
    Mark Review
    Given two independent events, if the probability that exactly one of them occurs is
    26
    49
     and the probability that none of them occurs is
    15
    49
    ,     then the probability of more probable of the two events is:
    [Online April 22, 2013]
    Given two independent events, if the probability that exactly one of them occurs is
    26
    49
     and the probability that none of them occurs is
    15
    49
    ,     then the probability of more probable of the two events is:
    [Online April 22, 2013]
  • Question 152/182
    4 / -1
    Mark Review
    The probability of a man hitting a target is
    2
    5
    . He fires at the target k times (k, a given number ). Then the minimum k, so that the probability of hitting the target at least once is more than
    7
    10
    ,     is :
    [Online April 9, 2013]
    The probability of a man hitting a target is
    2
    5
    . He fires at the target k times (k, a given number ). Then the minimum k, so that the probability of hitting the target at least once is more than
    7
    10
    ,     is :
    [Online April 9, 2013]
  • Question 153/182
    4 / -1
    Mark Review
    A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:
    [2013]
    A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:
    [2013]
  • Question 154/182
    4 / -1
    Mark Review
    There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is
    [Online May 26, 2012]
    There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is
    [Online May 26, 2012]
  • Question 155/182
    4 / -1
    Mark Review
    If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is
    [Online May 19, 2012]
    If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is
    [Online May 19, 2012]
  • Question 156/182
    4 / -1
    Mark Review
    A number n is randomly selected from the set {1,2,3,......,1000}. The probability that
    n
    ∑
    i=1
    i2
    n
    ∑
    i=1
    i
     is an integer is
    [Online May 12, 2012]
    A number n is randomly selected from the set {1,2,3,......,1000}. The probability that
    n
    ∑
    i=1
    i2
    n
    ∑
    i=1
    i
     is an integer is
    [Online May 12, 2012]
  • Question 157/182
    4 / -1
    Mark Review
    Let X and Y are two events such that P(X∪Y)=P(X∩Y)
    Statement 1: P(X∩Y′)=P(X′∩Y)=0
    Statement 2: P(X)+P(Y)=2P(X∩Y)
    [Online May 7, 2012]
    Let X and Y are two events such that P(X∪Y)=P(X∩Y)
    Statement 1: P(X∩Y′)=P(X′∩Y)=0
    Statement 2: P(X)+P(Y)=2P(X∩Y)
    [Online May 7, 2012]
  • Question 158/182
    4 / -1
    Mark Review
    Three numbers are chosen at random without replacement from {1,2,3,..8}. The probability that their minimum is 3 , given that their maximum is 6 , is :
    [2012]
    Three numbers are chosen at random without replacement from {1,2,3,..8}. The probability that their minimum is 3 , given that their maximum is 6 , is :
    [2012]
  • Question 159/182
    4 / -1
    Mark Review
    Let A,B,C, be pairwise independent events with P(C)>0and P(A∩B∩C)=0. Then P(Ac∩Bc∕C).
    [2011RS]
    Let A,B,C, be pairwise independent events with P(C)>0and P(A∩B∩C)=0. Then P(Ac∩Bc∕C).
    [2011RS]
  • Question 160/182
    4 / -1
    Mark Review
    If C and D are two events such that C⊂D and P(D)≠0 then the correct statement among the following is
    [2011]
    If C and D are two events such that C⊂D and P(D)≠0 then the correct statement among the following is
    [2011]
  • Question 161/182
    4 / -1
    Mark Review
    Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to
    31
    32
    ,     then p lies in the interval
    [2011]
    Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to
    31
    32
    ,     then p lies in the interval
    [2011]
  • Question 162/182
    4 / -1
    Mark Review
    Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ...20}.
    Statement -1: The probability that the chosen numbers when arranged in some order will form an AP is
    1
    85
    .
    Statement -2 : If the four chosen numbers form an AP, then the set of all possible values of common difference is ( ±1, ±2, ±3, ±4, ±5) .
    [2010]
    Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ...20}.
    Statement -1: The probability that the chosen numbers when arranged in some order will form an AP is
    1
    85
    .
    Statement -2 : If the four chosen numbers form an AP, then the set of all possible values of common difference is ( ±1, ±2, ±3, ±4, ±5) .
    [2010]
  • Question 163/182
    4 / -1
    Mark Review
    An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
    [2010]
    An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
    [2010]
  • Question 164/182
    4 / -1
    Mark Review
    One ticket is selected at random from 50 tickets numbered 00,01,02,.....,49. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals:
    [2009]
    One ticket is selected at random from 50 tickets numbered 00,01,02,.....,49. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals:
    [2009]
  • Question 165/182
    4 / -1
    Mark Review
    In a binomial distribution B(n,p=
    1
    4
    )    , if the probability of at least one success is greater than or equal to
    9
    10
    ,     then n is greater than:
    [2009]
    In a binomial distribution B(n,p=
    1
    4
    )    , if the probability of at least one success is greater than or equal to
    9
    10
    ,     then n is greater than:
    [2009]
  • Question 166/182
    4 / -1
    Mark Review
    A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A∪B) is
    [2008]
    A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A∪B) is
    [2008]
  • Question 167/182
    4 / -1
    Mark Review
    It is given that the events A and B are such that P(A)=
    1
    4
    ,P(A|B)=
    1
    2
     and P(B|A)=
    2
    3
    .     Then P(B) is
    [2008]
    It is given that the events A and B are such that P(A)=
    1
    4
    ,P(A|B)=
    1
    2
     and P(B|A)=
    2
    3
    .     Then P(B) is
    [2008]
  • Question 168/182
    4 / -1
    Mark Review
    Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
    [2007]
    Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
    [2007]
  • Question 169/182
    4 / -1
    Mark Review
    A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
    [2007]
    A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
    [2007]
  • Question 170/182
    4 / -1
    Mark Review
    At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is
    [2006]
    At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is
    [2006]
  • Question 171/182
    4 / -1
    Mark Review
    Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
    [2005]
    Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
    [2005]
  • Question 172/182
    4 / -1
    Mark Review
    Let A and B be two events such that P(A∪B)=
    1
    6
    ,P(A∩B)=
    1
    4
     and P(A)=
    1
    4
    ,     where A stands for complement of event A. Then events A and B are
    [2005]
    Let A and B be two events such that P(A∪B)=
    1
    6
    ,P(A∩B)=
    1
    4
     and P(A)=
    1
    4
    ,     where A stands for complement of event A. Then events A and B are
    [2005]
  • Question 173/182
    4 / -1
    Mark Review
    A random variable X has Poisson distribution with mean 2 . Then P(X>1.5) equals
    [2005]
    A random variable X has Poisson distribution with mean 2 . Then P(X>1.5) equals
    [2005]
  • Question 174/182
    4 / -1
    Mark Review
    The probability that A speaks truth is
    4
    5
    ,     while the probability for B is
    3
    4
    .     The probability that they contradict each other when asked to speak on a fact is
    [2004]
    The probability that A speaks truth is
    4
    5
    ,     while the probability for B is
    3
    4
    .     The probability that they contradict each other when asked to speak on a fact is
    [2004]
  • Question 175/182
    4 / -1
    Mark Review
    The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
    [2004]
    The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
    [2004]
  • Question 176/182
    4 / -1
    Mark Review
    A random variable X has the probability distribution:

    For the events E={X is a prime number } and F={X<4}, the P(E∪F) is
    [2004]
    A random variable X has the probability distribution:

    For the events E={X is a prime number } and F={X<4}, the P(E∪F) is
    [2004]
  • Question 177/182
    4 / -1
    Mark Review
    Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
    [2003]
    Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
    [2003]
  • Question 178/182
    4 / -1
    Mark Review
    Events A,B,C are mutually exclusive events such that P(A)=
    3x+1
    3
    ,P(B)=
    1−x
    4
     and P(C)=
    1−2x
    2
     The setof possible values of x are in the interval.
    [2003]
    Events A,B,C are mutually exclusive events such that P(A)=
    3x+1
    3
    ,P(B)=
    1−x
    4
     and P(C)=
    1−2x
    2
     The setof possible values of x are in the interval.
    [2003]
  • Question 179/182
    4 / -1
    Mark Review
    The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X=1) is
    [2003]
    The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X=1) is
    [2003]
  • Question 180/182
    4 / -1
    Mark Review
    A and B are events such that P(A∪B)=3∕4,P(A∩B)=1∕4,P(A)=
    2
    3
     then P(A∩B) is
    [2002]
    A and B are events such that P(A∪B)=3∕4,P(A∩B)=1∕4,P(A)=
    2
    3
     then P(A∩B) is
    [2002]
  • Question 181/182
    4 / -1
    Mark Review
    A problem in mathematics is given to three students A,B, C and their respective probability of solving the problem is
    1
    2
    ,
    1
    3
     and
    1
    4
    .     Probability that the problem is solved is
    [2002]
    A problem in mathematics is given to three students A,B, C and their respective probability of solving the problem is
    1
    2
    ,
    1
    3
     and
    1
    4
    .     Probability that the problem is solved is
    [2002]
  • Question 182/182
    4 / -1
    Mark Review
    A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
    [2002]
    A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
    [2002]
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