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Probability Test 6
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Probability Test 6
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  • Question 1/10
    1 / -0

    Direction (1-3): An urn contain 6 orange, 4 green,3 pink and 4 black balls

    If 3 balls are picked at random, what is the probability that all are pink ?

    Solutions

    Explanation :

    17C3 = 17*16*15/3*2*1 = 4080/6 = 680

    3C3 = 1

    P = 1/680

     

  • Question 2/10
    1 / -0

    Direction (1-3): An urn contain 6 orange, 4 green,3 pink and 4 black balls

    If 5 balls are picked at random, what is the probability that none are orange ?

    Solutions

    Explanation :

    17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188

    11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462

    P = 462/6188 = 33/442

     

  • Question 3/10
    1 / -0

    Direction (1-3): An urn contain 6 orange, 4 green,3 pink and 4 black balls

    If 3 balls are drawn at random, what is the probability that 1 is green and the other 2 are black ?

    Solutions

    Explanation :

    17C3 = 17*16*15/3*2*1 = 4080/6 = 680

    4C1 × 4C2 = 4*4*3/2*1 = 24

    P = 24/680 = 3/85

     

  • Question 4/10
    1 / -0

    There are 8 positive numbers and 6 negative numbers. 4 numbers are chosen at random and multiplied. Find the probability that the product is a positive number ?

    Solutions

    Explanation :

    14C4  = 14*13*12*11/4*3*2*1 = 1001

    4 No positive+4 no negative + (2 no positive * 2 no negative)

    = 6C4 + 8C4 +(6C2 ×8C2) = 15+70+15*28 = 505

    P = 505/1001

     

  • Question 5/10
    1 / -0

    A five digit number is formed with the digit 1,2,3,4 and 5 without repetition. Find the chance that the number is divisible by 5 ?

    Solutions

    Explanation :

    5! = 5*4*3*2*1 = 120

    4! = 4*3*2*1 = 24

    P = 24/120 = 1/5

     

  • Question 6/10
    1 / -0

    A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?

    Solutions

    Explanation :

    13C2 = 13*12/2 =78

    2C2 = 1

    P = 1/78

     

  • Question 7/10
    1 / -0

    If You toss a coin and roll a die. What is the probability of getting a head and a 3 on the die?

    Solutions

    Explanation :1/2 * 1/6 = 1/12

     

  • Question 8/10
    1 / -0

    From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

    Solutions

    Explanation :

    =4C1×4C1×4C1 / 52C3

    =4×4×4 / 22100

    =16/5525

     

  • Question 9/10
    1 / -0

    Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

    Solutions

    Explanation :

    n(S) = 36

    n(E) = (2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(6,2),(3,4),(6,4),(3,6)

    P = 11/36

     

  • Question 10/10
    1 / -0

    Two dice are tossed. The probability that the total score is a prime number is

    Solutions

    Explanation :

    E =  (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),

    (5, 2), (5, 6), (6, 1), (6, 5)

    n(E) = 15

    n(S) = 6*6 = 36

    P = 15/36 = 5/12

     

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