MathDB
2018 PUMaC Live Round 2.3

Source:

January 13, 2019
PuMACLive Roundcountingdistinguishabilityprobabilityexpected value

Problem Statement

Sophie has 2020 indistinguishable pairs of socks in a laundry bag. She pulls them out one at a time. After pulling out 3030 socks, the expected number of unmatched socks among the socks that she has pulled out can be expressed in simplest form as mn\tfrac{m}{n}. Find m+nm+n.