Question

A drawer contains 8 black socks and 8 white. Two are pulled out randomly: I) probability that it is the same colour? II) how many will have to be pulled out for matching pairs?

Answer 1

(I) `7/15`; (II) `3` socks.

Explanation:

Let `B` denote pulling out a black sock and `W` denote pulling out a white sock from the drawer.

When two socks are pulled out randomly, the possibility that they are of same color would be when we pull out `BB` or `WW`.

(I) As there are `8` black socks and `8` white socks,

the probability of pulling out one black sock is `8/16` and pulling out another black will be `7/15`, as we are left with `15` socks with `7` black socks.

Hence probability of pulling out pair of black socks is `8/16xx7/15=7/30`

Similarly probability of pulling out pair of white socks too is `8/16xx7/15=7/30`

and hence the probability that it is the same color is `14/30=7/15`

(II) We must pull out three socks so that they are matching pairs. Observe that in such a case even if first two socks (if they are of same color, we are done) are of different colors, third must be of either color and we have got a matching pair.