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4 November, 08:24

A bowl contains 8 chips: 4 blue and 4 red. Three chips are drawn at random and without replacement from a bowl. What is the probability that all three chips chosen?

a. 1/4

b. 1/8

c. 1/10

d. 1/13

e. 1/15

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Answers (1)
  1. 4 November, 09:20
    0
    the probability that 3 blue chips (or red chips) are chosen is P (X=3) = 1/14

    Step-by-step explanation:

    Since the X = choosing x blue chips, then P (X) follows an hypergeometric distribution, when sampling is done without replacement

    P (X=x) = (C, x) * (N-C, n-x) / (N, n)

    where () represents combinations then

    N = population size = 8 chips

    n = sample size = 3 chips

    C = number of blue chips = 4 chips

    x = number of blue chips that are chosen = 3 blue chips

    replacing values

    P (X=3) = (4,3) * (8-4, 3-3) / (8,3) = (4,3) * (4, 0) / (8,3) = 4 * 1 / [ 8! / (3!*5!) ] =

    4*3!*5! / 8! = 1/14

    P (X=3) = 1/14
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