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Math Help - probability

  1. #1
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    probability

    Hey guys i need help wiht this problem:

    Suppose that two evenly matched teams play in the best-of-seven NBA Finals (This means that the first team to win four games wins the championship). They are so evenly matched that the probability of either teamís winning any particular game is precisely 50 percent. Not only that, the teams donít get overconfident or discouraged, so the 50 percent probability doesnít change as the Finals progress.
    Under these conditions, it is quite unlikely that either team will engineer a four-game sweep. In fact it turns out that a sweep is one-half as likely as the Finals ending in five games.
    What is the probability that the Finals will go the full seven games?

    thanks
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  2. #2
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    Quote Originally Posted by anime_mania View Post
    Hey guys i need help wiht this problem:

    Suppose that two evenly matched teams play in the best-of-seven NBA Finals (This means that the first team to win four games wins the championship). They are so evenly matched that the probability of either teamís winning any particular game is precisely 50 percent. Not only that, the teams donít get overconfident or discouraged, so the 50 percent probability doesnít change as the Finals progress.
    Under these conditions, it is quite unlikely that either team will engineer a four-game sweep. In fact it turns out that a sweep is one-half as likely as the Finals ending in five games.
    What is the probability that the Finals will go the full seven games?

    thanks
    This sounds like a binomial probability.

    We want each of the teams to win exactly three of the six first games.
    What happens in the seventh doesn't matter


    f(x) = \binom{6}{3}\left( \frac{1}{2}\right)^3 \left( \frac{1}{2}\right) ^3=\frac{5}{16}
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