In your sock drawer there are 15 distinct pairs of socks and

In your sock drawer, there are 15 distinct pairs of socks (and two socks in the same pair look alike). If you are searching for a matching pair in the dark, what is the minimum number of individual socks that you must pull out to guarantee that you have at least one matching pair? Your favorite pair has Buzz on them. How many individual socks must you pull out to guarantee that you selected both socks in your favorite pair?

Solution

If we pull out 15 socks, they may all be from different pairs. So, for 1st part, we need to pull out atleast 16 times to get a pair because the 16th sock will match with atleast one other.

For second part, to get both buzz socks, we need to pull atleast 30 socks because first buzz sock will appear within 15 attempts but the second one might not appear untill last sock is pulled.