- #1

Yankel

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I wasn't sure if this question should be placed here or on algebra forum, but it is related to probability, so I put it here.

A basketball player shoots several times during some time period in a game, and scores less than 80% of his shots (let's say after the first quarter, but the time doesn't really matters). At the end of the game, he scored more than 80% of his shots. Is it necessary that at some point during the game, his success was exactly 80% ?

My intuition say that the answer is no, because this is not a continuous function, but every example I tried setting up, showed that 80% was achieved. What do you think ?