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Math Help - How to apply Bayes theorem to this situation

  1. #1
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    How to apply Bayes theorem to this situation

    Here is the problem.
    (The situation is real, so the real initials of the jockey and trainer are used in the problem to keep my personal level of confusion to minimum.)

    CR is a jockey riding at a racetrack.
    PS is a trainer training at the same place.
    CR is occasionally engaged by PS to ride his horses.
    Here are the statistics for the current season as they stand right now.

    Jockey CR has 22 winners from 109 rides.
    Trainer PS has 17 winners from 68 runners.
    CR has ridden 19 runners trained by PS and has won with 6 of them.

    On today's card, CR is engaged to ride two horses trained by PS, say in the 2nd and in the 5th race. For simplicity's sake, we assume that PS has only these two runners on today's card, and even CR has only these two rides for the day.

    Based on this data, what is the probability of CR riding a winner for PS in the 2nd race?

    Next what is the revised probability of CR riding a winner for PS in the 5th race when:
    a) the 2nd race horse is a winner
    b) the 2nd race horse is a loser

    Note: I am new to this forum, and also newly initiated in the Bayesian methods. So please allow your explanations to be as detailed as possible to have a better chance of me understanding it.

    Thanks in advance.

    Dhru
    Last edited by dhrutika; October 25th 2008 at 07:48 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dhrutika View Post
    Here is the problem.
    (The situation is real, so the real initials of the jockey and trainer are used in the problem to keep my personal level of confusion to minimum.)

    CR is a jockey riding at a racetrack.
    PS is a trainer training at the same place.
    CR is occasionally engaged by PS to ride his horses.
    Here are the statistics for the current season as they stand right now.

    Jockey CR has 22 winners from 109 rides.
    Trainer PS has 17 winners from 68 runners.
    CR has ridden 19 runners trained by PS and has won with 6 of them.

    On today's card, CR is engaged to ride two horses trained by PS, say in the 2nd and in the 5th race. For simplicity's sake, we assume that PS has only these two runners on today's card, and even CR has only these two rides for the day.

    Based on this data, what is the probability of CR riding a winner for PS in the 2nd race?

    Next what is the revised probability of CR riding a winner for PS in the 5th race when:
    a) the 2nd race horse is a winner
    b) the 2nd race horse is a loser

    Note: I am new to this forum, and also newly initiated in the Bayesian methods. So please allow your explanations to be as detailed as possible to have a better chance of me understanding it.

    Thanks in advance.

    Dhru
    Bayes theorem does not tell us anything for this problem. All of this data is consistent with there being no dependence on ride or trainer and that the probability of a horse of PS winning is ~25%.

    Also there is no data that allows conclusion about the correlation of the result of one race with another to be drawn.

    CB
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  3. #3
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    What if

    Quote Originally Posted by CaptainBlack View Post
    Bayes theorem does not tell us anything for this problem. All of this data is consistent with there being no dependence on ride or trainer and that the probability of a horse of PS winning is ~25%.

    Also there is no data that allows conclusion about the correlation of the result of one race with another to be drawn.

    CB
    Thanks CB.

    Now if there is additional information that 1,198 horses have run so far this racing season (let us assume each horse has run only once), do you think now Bayes theorem can be applied?

    Dhru
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by dhrutika View Post
    Thanks CB.

    Now if there is additional information that 1,198 horses have run so far this racing season (let us assume each horse has run only once), do you think now Bayes theorem can be applied?

    Dhru
    No, it give no additional information.

    CB
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