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Thread: (Simple) World series probability question?

  1. #1
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    (Simple) World series probability question?

    In the World Series, two teams play each other until one team wins 4 games. How many different series of games is possible? (i.e., Team A wins the series by winning games 1, 2, 4, and 6)

    Would it just be 7 choose 4?
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    Quote Originally Posted by jellyksong View Post
    In the World Series, two teams play each other until one team wins 4 games. How many different series of games is possible? (i.e., Team A wins the series by winning games 1, 2, 4, and 6)
    Would it just be 7 choose 4?
    This is perhaps the most famous question in probability.
    It may well date back to the eleventh centenary.
    Playing any series of seven games will determine a winner. RIGHT?
    “Who has four wins, there are no ties’s”.
    $\displaystyle \sum\limits_{k = 4}^7 {\binom{7}{k}2^{ - k} } = 0.5$ for each team.
    Last edited by Plato; Mar 14th 2011 at 04:44 AM. Reason: correction
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  3. #3
    Super Member Random Variable's Avatar
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    If Team A wins in 4 games, they must win the first three games. If Team A wins in 5 games, they must win 3 out of the first 4 games. If Team A wins in 6 games, they must win 3 out of first 5 games. And if team A wins in 7 games, they must win 3 out of the first 6 games.

    So number of ways Team A wins is $\displaystyle \binom{3}{3} + \binom{4}{3} + \binom{5}{3} + \binom{6}{3} $

    And the number of ways Team B can win is obviously the same.
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    Quote Originally Posted by Random Variable View Post
    If Team A wins in 4 games, they must win the first three games. If Team A wins in 5 games, they must win 3 out of the first 4 games. If Team A wins in 6 games, they must win 3 out of first 5 games. And if team A wins in 7 games, they must win 3 out of the first 6 games.So number of ways Team A wins is $\displaystyle \binom{3}{3} + \binom{4}{3} + \binom{5}{3} + \binom{6}{3} $ And the number of ways Team B can win is obviously the same.
    Do you understand that none of that makes any difference?
    Team A wins if any of the sequences $\displaystyle AAAABBB$ occurs?
    Suppose that we require that seven games be played period no matter the outcomes. Do you see that any string of four A's and three B's mans that team A wins?
    As I said above, this question has a long history.
    I can trace it back ot at least the $\displaystyle 11^{th}$ century.
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  5. #5
    Super Member Random Variable's Avatar
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    Well, the answer you posted makes no sense. Team A wins in 35/16 ways?

    EDIT: Did you mean $\displaystyle \binom{7}{4} $ ways?
    Last edited by Random Variable; Mar 13th 2011 at 08:32 PM.
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