Suppose that on the morning after these games the, Ask an Expert

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A city has a professional basketball team playing at home and a professional hockey team playing away on the same night . A professional basketball team has a 0.641 probability of winning a home game and a professional hockey tem has 0.462 probability of winning an away game . Historically , when both teams play on the same night , the chance that the next morning's leading sports story will be about the basketball game is 60% and the chance that it will be about the hockey game is 40%.
Suppose that on the morning after these games the newspaper's leading sports story begins with the headline " We Win...." What is the probability that the story is about the basketball team?

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