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Question: 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 p1 of getting it right. Each time B plays, he has probability p2 of getting it right.
(a) If A answers m questions, what is the PMF of the number of questions she gets right?
(b) If A answers m times and B answers n times, what is the PMF of the total number of questions they get right (you can leave your answer as a sum)? Describe exactly when/whether this is a Binomial distribution.
(c) 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.
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