Question

I'm getting dressed in the dark, and I have 6 pairs of white socks and 6 pairs of black socks, but they're all mixed up in my sock drawer. How many socks will I need to blindly pull out to ensure that I get five pairs of white socks?

Answer 1

Answer:

We'll need to pull out 11 pairs of socks to be sure to get five pairs of white socks.

Step-by-step explanation:

Combinations

We have 6 pairs of white socks and 6 pairs of black socks. If we wanted to pull out five pairs of white socks, there are to extreme scenarios:

The most favorable event is to take the five pairs in the first five takes. But that won't be for sure.

The worst case would be to take all the black socks first, and then take the five white socks. It would be a sure event and we must assume it as a possibility. Thus:

We'll need to pull out 11 pairs of socks to be sure to get five pairs of white socks