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You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them type 1), 0.4 against a

You enter a chess tournament where your probability of winning a game is 0.3 against half the players (call them type 1), 0.4 against a quarter of the players (call them type 2), and 0.5 against the remaining quarter of the players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning?

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