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# Probability Distribution for a Basketball Game

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At the end of a basketball game, a team is down by 1 point. As the last play, a player from that team throws a three-point shot that misses, but the player is fouled and he gets to take 3 free throws (each worth 1 point) to end the game. On any given free throw, the probability that the player makes the shot is twice as large as the probability that he misses the shot. Write out the sample space of all possible outcomes from the three free throws, and then calculate the probability distribution of all values of the random variable X = number of successful free throws made.

Answer the following two questions using the probability distribution calculated above

a) If a game is tied at the end of regulation, the two teams play an overtime
period. What is the probability that the player forces an overtime period?
b) What is the probability that team A wins in regulation?