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Probability Test 9
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Probability Test 9
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  • Question 1/19
    1 / -0

    A box contain 4 white, 3 blue and 2 black marbles. If 2 marbles are picked up at random. What is the probability that both of them are black ?

    Solutions

    Explanation :

    P = 2C2/9C2 = 1/36

     

  • Question 2/19
    1 / -0

    An urn contains 6 maroon, 3 pink and 4 white balls. If three balls are drawn What is the probability that all are pink or white?

    Solutions

    Explanation :

    P =3C3/13C3 + 4C3/13C3

    = 1/286 + 4/286 = 5/26

     

  • Question 3/19
    1 / -0

    From a pack of 52 cards 3 cards are drawn one by one without replacements.Find the probability that both of them are king ?

    Solutions

    Explanation :

    4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525

     

  • Question 4/19
    1 / -0

    If two dice are thrown simultaneously, what is the probability that the sum of the numbers appeared is less than seven?

    Solutions

    Explanation :

    Sum of the numbers can be 1,2, 3, 4, 5, and 6.

    1+2=  3

    1+3 = 4

    1+4 = 5

    1+5 = 6

    2+3 = 5

    3+2 = 5

    2+4 = 6

    4+2 = 6……..etc

    n (E) = 15, n (S) = 36

    P (E) =15/36  = 5/12

     

  • Question 5/19
    1 / -0

    A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green ?

    Solutions

    Explanation :

    4C2+(4C1*10C1)/12C2 = 6+40/91 = 46/91

     

  • Question 6/19
    1 / -0

    In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK ?

    Solutions

    Explanation :

    P = 6/18 = 1/3

     

  • Question 7/19
    1 / -0

    A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?

    Solutions

    Explanation :

    P = 4C1*8C3/12C4 = 4*56/495 = 224/495

     

  • Question 8/19
    1 / -0

    A bag contains 4 white, 8 black and 6 blue balls. If two balls are drawn at random, find the probability of both the balls being black?

    Solutions

    Explanation :

    n(S) = 18C2 = 153

    There are eight black balls, out of which two balls are drawn in 8C2 ways.

    n(E) = 28

    P(E) = 28 /153 = 28/153

     

  • Question 9/19
    1 / -0

    The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?

    Solutions

    Explanation :

    5:2 = 15+6 = 21

    n(S) = 21C3 = 1330

    n(E) = 15C1 × 6C2 = 15 × 15 = 225

    P = 225/1330 = 45/266

     

  • Question 10/19
    1 / -0

    A bag 5 red and 8 white balls.Two draws of three balls each are made.What is the probability that the balls were pink in the first draw and white in the second draw ?

    Solutions

    Explanation :

    5C3/13C3 *8C3/13C3 = 60/286*56/286 = 140/20449

     

  • Question 11/19
    1 / -0

    A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?

    Solutions

    Explanation

    From 1 to 24, there are 8 numbers which are multiple of 3

    Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets

    8C2*16C1 / 24C3 = 56/253

    Case 2: all are multiples of 3.

    8C3 / 24C3 = 7/253

    Add both cases.

     

  • Question 12/19
    1 / -0

    A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball? 

    Solutions

    Explanation: 

    Total balls = 15

    Not red means green or blue i.e. any of (5+6) = 11 balls

    So prob. = 11C2 / 15C2

     

  • Question 13/19
    1 / -0

    From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or  heart card? 

    Solutions

    Explanation: 

    Prob. of black card:

    26C2 / 52C2 = 25/102

    Prob. of heart card:

    13C2 / 52C2 = 3/51

    Add both cases.

     

  • Question 14/19
    1 / -0

    From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children? 

    Solutions

    Explanation: 

    Case 1: Prob. when 2 men, 1 woman and 1 child

    3C2*4C1*2C1 /9C4 = 4/21

    Case 2: Prob. when 1 man, 2 women and 1 child

    3C1*4C2*2C1 /9C4 = 2/7

    Case 3: Prob. when 1 man, 1 woman and 2 children

    3C1*4C1*2C2 /9C4 = 2/21

     

  • Question 15/19
    1 / -0

    A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb? 

    Solutions

    Explanation:

    5C1*20C2/25C3

     

  • Question 16/19
    1 / -0

    There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball? 

    Solutions

    Explanation: 

    Case 1: 0 green ball means all three red or white balls

    9C3/12C3

    Case 2: 1 green ball and two red or white balls

    9C2*3C1/12C3

    Add both cases.

     

  • Question 17/19
    1 / -0

    A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color? 

    Solutions

    Explanation: 

    This will be = 1- prob.(both are same in color)

    Prob. of both same in color = [3C2+4C2+3C2]/10C2 = 12/45

    So required prob. = 1 – 12/45

     

  • Question 18/19
    1 / -0

    There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?

    Solutions

    Explanation: 

    When both black, prob. = 4/10 * 3/9

    When both white, prob. = 6/10 * 5/9

    Add both cases.

     

  • Question 19/19
    1 / -0

    A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color? 

    Solutions

    Explanation: 

    Case 1: both red

    5C2/9C2

    Case 2: both green

    4C2/9C2

    Add both cases.

     

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