Draw balls from two bags, i need the expected value? Assume we have $2$ bags with $3$ colors balls, each bag has $n$ balls so $n/3$ of each color. if we take one ball from each bag then place them aside until we took ...--prophetes.ai

Draw balls from two bags, i need the expected value? Assume we have $2$ bags with $3$ colors balls, each bag has $n$ balls so $n/3$ of each color. if we take one ball from each bag then place them aside until we took them all, what is the expected value of the number of matching balls? bags setup

Hint: What is the chance the first pair matches? Every pair has the same chance to match-imagine reordering the draws to bring each pair to the front. Therefore the expected number of matches is ???