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Math Help - (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”.
    \sum\limits_{k = 4}^7 {\binom{7}{k}2^{ - k} }  = 0.5 for each team.
    Last edited by Plato; March 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  \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  \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 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 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  \binom{7}{4} ways?
    Last edited by Random Variable; March 13th 2011 at 08:32 PM.
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