Question

Justin has 10 loose socks in a drawer, forming 5 pairs. But Justin is careless and chooses two socks at random. What is the probability that they will match?

Answer 1

Suppose we assign the pair of socks as : a,b,c,d,and e

Since there are two socks in any pair , so that the probability of selection of any specified socks = 1/10

Therefore the probability of selection of another socks of same specification of the first socks is = ( 2 - 1)/ (10 - 1) = 1/9

So the probability of selection of any specified pair that they will match = (1/10)*(1/9) = 2/90

But there are total five pairs of socks.

So the probability of selection two socks that they will match = 5*(2/90) = 1/9 = 0.1111 (This is the final answer).