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

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