Players A and B take turns in answering trivia questions, starting with player A answering the first question. Each time A answers a question, she has probability $p\_1$ of getting it right. Each time B plays, he has probability $p\_2$ of getting it right. 

Suppose that the first player to answer correctly wins the game (with no predetermined maximum number of questions that can be asked). Find the probability that A wins the game.

Can someone post step-by-step solution? This is a question from Joe Blitzstein's Stat 110 homework question