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Math Help - Please help me calculate this probability

  1. #1
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    Please help me calculate this probability

    Hi.

    I'm struggling to get my head round this issue I'm discussing with friends.

    It regards the chances of any of the top 4 teams from last season in a league playing each other on the same day.

    So, assuming 20 teams (they play twice, home and away) who each play on the same day once a week for 38 weeks, what is the chance that the teams who finished in positions 1-4 last season, will play each other on the same day at any point in the season given a random fixture draw.

    I've been told 17% but that seems too low to me.

    Can anyone explain how this would be calculated?

    Thanks.
    Last edited by McGraw; November 11th 2008 at 02:16 AM.
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  2. #2
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    Quote Originally Posted by McGraw View Post
    Hi.

    I'm struggling to get my head round this issue I'm discussing with friends.

    It regards the chances of any of the top 4 teams from last season in a league playing each other on the same day.

    So, assuming 20 teams (they play twice, home and away) who each play on the same day once a week for 38 weeks, what is the chance that the teams who finished in positions 1-4 last season, will play each other on the same day at any point in the season given a random fixture draw.

    I've been told 17% but that seems too low to me.

    Can anyone explain how this would be calculated?

    Thanks.
    Hi McGraw,

    Let's say the 4 teams are A, B, C, and D, and let's assume the matches are chosen by random draw each week. On any given week, then, the probability that A will play one of B, C, or D is 3/19, because there are 19 other teams and they are all equally likely to be chosen. Let's say, for example, that A plays B. Then the probability that C will play D is 1/17 by similar reasoning. So the probability that the 4 teams will play each other on any given week is (3/19) * (1/17) = 3/323.

    Since there are 38 weeks, the probability that the 4 teams will NOT play each other at all is (1 - 3/323)^{38}, and the probability that they will play each other at least once in 38 weeks is
    1 - (1 - 3/323)^{38} = 0.2985.
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  3. #3
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    Thanks very much.
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