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Question: problem 1 you enter a chess tournament where your probability...

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Problem 1. You enter a chess tournament where your probability of winning a game is 0.54 against 20% the players (call them type 1), 0.31 against other 10% of the players (call them type 2), and 0.15 against the remaining 70% players (call them type 3) (a) You play a game against a randomly chosen opponent. What is the probability of winning? (b) Suppose that you were the winner of a game. What is the probability that your oppo- nent was of type 3?

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