Question

A man has 3 pairs of black socks and 2 pair of brown socks . If he dresses up hurriedly in the dark , find the probability that after he has put a black sock , he will put on another black sock

Answer 1

we want a match here. if we pick 2 socks from 5 brown socks then there will be a match.

no. of ways of picking 2 out of 9 socks= 9C2 ways = 36 ways

no. of ways of picking 2 out of 5 brown socks= 5C2= 10 ways.

again if we pick 2 socks from 4 green socks then there also will be a match.

no. of ways of picking 2 out of 4 green socks= 4C2= 6 ways.

total no. of ways in which we can pick a match =10 +6= 16 ways

so desired probability is 16/36 = 4/9