Question 105
Let $p$ and $q$ be positive real numbers with $p+q\lt 1$. Teams $A$ and $B$ play a series of games. For each game, $A$ wins with probability $p$, $B$ wins with probability $q$, and they tie with probability $1-p-q$. The series ends when one team has won two more games than the other, that team being declared the winner of the series. What is the probability that $A$ wins the series?