A drawer contains 6 black socks 4 gray socks and 2 blue sock

A drawer contains 6 black socks, 4 gray socks and 2 blue socks. You randomly choose 1 sock from the drawer, then randomly choose a second sock after replacing the first sock. What is the probability that both socks are gray?

Solution

Given

black socks = 6

gray socks = 4

blue socks = 2

Total socks = 6 + 4 + 2 = 12

now

probability of choosing a gray sock initially = number of gray socks / total number of socks = 4 / 12 = 1 / 3

as the socks is replaced so there will be same number of socks when we draw 2^nd time and the probability is same as 1^st = 1 / 3

probability that both socks are gray = (1 / 3) * (1 / 3) = 1 / 9 =0.1111

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