Question

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

Answer 1

the probability that 3 blue chips ( or red chips) are chosen is P(X=3) = 1/14

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