Two basketball players play a game in which they alternately shoot a basketball at a hoop. The first one to make a basket wins the game. On each shot, Player 1 (the one who shoots first) has probability P1 of success, while Player 2 has probability p2 of success (assume 0 < P1, P2 < 1). The shots are assumed to be independent. a. Find P(W1), the probability that Player 1 wins the game. b. For what values of pi and p2 is this a fair game, i.e., each player has a 50 percent chance of winning the game?

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Two basketball players play a game in which they alternately shoot a basketball at a hoop. The first
one to make a basket wins the game. On each shot, Player 1 (the one who shoots first) has probability
Pi of success, while Player 2 has probability p2 of success (assume 0 < p1, P2 < 1). The shots are
assumed to be independent.
a. Find P(W1), the probability that Player 1 wins the game.
b. For what values of pi and p2 is this a fair game, i.e., each player has a 50 percent chance of
winning the game?
Transcribed Image Text:Two basketball players play a game in which they alternately shoot a basketball at a hoop. The first one to make a basket wins the game. On each shot, Player 1 (the one who shoots first) has probability Pi of success, while Player 2 has probability p2 of success (assume 0 < p1, P2 < 1). The shots are assumed to be independent. a. Find P(W1), the probability that Player 1 wins the game. b. For what values of pi and p2 is this a fair game, i.e., each player has a 50 percent chance of winning the game?
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