TxO Math Bowl 2024 - Guts Contest - Set 3 Problem 3

Let there be 6 magical fish that in a tank, 3 of them are male, and 3 of them are female. A breeder arbitrarily puts the 6 fish into 3 fish bowls such that each bowl houses 2 fish. If the two fish in each bowl are of opposite sex, they instantly fall in love (W Rizz) and immediately give birth to a baby fish. Otherwise, nothing will happen. If the expected value of the total number of fish, after they are placed into their bowls, allowed to fall in love, and give birth, can be expressed as \frac{m}{n}, where m and n are relatively prime positive integers, find m + n.