Question 10
Andrew and Bob alternate rounds, Andrew first. A bag contains $3$ white and $3$ black balls. The active player chooses a number from $2$ to $6$; the other draws that many balls without looking. The active player wins if more white than black are drawn. Otherwise all balls are returned and the other player becomes active. Both play optimally. If Bob’s winning probability is $a/b$ in lowest terms, find $a+b$.