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Math Help - help with "more than one event" probability

  1. #1
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    help with "more than one event" probability

    A baseball field is divided up into twelve regions for the purpose of notating
    where balls land. If each of the fi rst twelve balls hit into the field have an equal chance
    of landing in any of the regions, what is the probability that at least one region had
    more than one ball hit into it?

    I understand that the way to approach this problem is by subtracting the probability of hitting a ball into each region from 1, so 1 - P(ball hit in every region the first twelve balls), but am confused how to calculate that probability. Any help would be great!

    Thanks.
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  2. #2
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    Re: help with "more than one event" probability

    Quote Originally Posted by amma0913 View Post
    A baseball field is divided up into twelve regions for the purpose of notating where balls land. If each of the fi rst twelve balls hit into the field have an equal chance of landing in any of the regions, what is the probability that at least one region had more than one ball hit into it?

    There are \binom{12+12-1}{12} ways for the balls to land in the regions. There is only one way that each region will contain a ball.
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