A person keeps their socks in two drawers. Each drawer has 22 socks. The first drawer has 15 blue, 4 red, 3 yellow, and no green socks. The second drawer has 13 blue, 4 red, 2 yellow and 3 green socks.
They blindly take out one sock from the first drawer, and one from the second drawer, and put them to one side in a pair. They cant see which ones they took out. They repeat this process until they have 22 pairs, never putting any back in the drawers. What is the number of expected pairs?
Thank you so much! If you have any resources I should start with, please let me know:)
EDIT: Thank you for the tips and sorry this was asked so bluntly! I think if I just need to find the probability that any two socks are a match, it's like this
(15/22)(13/22)+(4/22)(4/22)+(3/22)(2/22) = 0.44834710743
Does that mean this same number applies to the expected percentage of pairs for all of the socks? Thank you again
The probability that you have found is the probability that the $i$th pair is a match, for any $i$ such that $1\le i\le 22$.
This is also the expected number of matches for the $i$th pair.
The expected number of matches over all the pairs is therefore the sum of these expectations
i.e. $22$ x $0.448347$.