Question

A sock drawer contains eight navy blue socks and five black socks with no other socks. If you reach in the drawer and take two socks without looking and without replacement, what is the probability that at least one navy sock will be selected?

Answer 1

The desired probability is `34/39`.

Explanation:

Let us first calculate the probability of selecting two black socks without looking and without replacement.

As there are `13` socks of which `5` are black, the probability of getting first black sock is `5/13`.

The probability of getting second sock too as black will then be `4/12=1/3` as now only four black socks out of `12` are left.

Hence probability of getting both socks as black is `5/13xx1/3=5/39`.

Hence, `1-5/39=34/39` is the probability that both socks are not black i.e. at least one sock is navy.