Manu has a pair of red socks and a pair of blue socks in his drawer. If he takes two socks out at random, what is the chance that they are a pair?
How many socks would he need to take out to be sure of getting a pair?
Solution:
After selecting the first sock, there are three remaining socks in the drawer and only one of these completes the pair. Therefore the chance of taking out a second sock at random and making a pair is 1/3.
There are 6 possibilities, all equally likely.
- Red 1 – Red 2
- Red 1 – Blue 1
- Red 1 – Blue 2
- Red 2 – Blue 1
- Red 2 – Blue 2
- Blue 1 – Blue 2
Only 2 of these are pairs (Red 1 – Red 2 and Blue 1 – Blue 2) so the probability of a pair is 2/6 or 1/3.
Manu’s first two selections could be a red sock and a blue sock (no pair) but his next pick must be the pair of one of the first two, so taking three socks would guarantee a pair.