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Math Help - Probability of a Goalkeeper being world class.

  1. #1
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    Smile Probability of a Goalkeeper being world class.

    Hi I'm new to this forum, but I could seriously do with some help guys.

    Okay so here's the question
    An ordinary goalkeeper has a 20% chance of saving a penalty. A world class goalkeeper has a 40% chance of saving a penalty. One in 10 professional goalskeepers are world- class.
    If I saw a goalkeeper saving a penalty, would I think that he was world-class? (I think I have to find P(A[B) using the Bayes' rule, where A is the goalkeeper being world class, and B him saving the penalty)

    An additional question is: If he saves the penalty in a row would you then think he was world class?

    Another additional question is: If he has 10 penalties taken against him, how many would he have to save for you to be 95% confident that he was world class?

    Any help would be great!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by IronMan View Post
    Hi I'm new to this forum, but I could seriously do with some help guys.

    Okay so here's the question
    An ordinary goalkeeper has a 20% chance of saving a penalty. A world class goalkeeper has a 40% chance of saving a penalty. One in 10 professional goalskeepers are world- class.
    If I saw a goalkeeper saving a penalty, would I think that he was world-class? (I think I have to find P(A[B) using the Bayes' rule, where A is the goalkeeper being world class, and B him saving the penalty)

    P(WC|S)= \frac{P(S|WC)P(WC)}{P(S)}=\frac{0.4\times 0.1}{0.4\times 0.1+0.2 \times 0.9}

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by IronMan View Post
    Hi I'm new to this forum, but I could seriously do with some help guys.

    Okay so here's the question
    An ordinary goalkeeper has a 20% chance of saving a penalty. A world class goalkeeper has a 40% chance of saving a penalty. One in 10 professional goalskeepers are world- class.
    If I saw a goalkeeper saving a penalty, would I think that he was world-class? (I think I have to find P(A[B) using the Bayes' rule, where A is the goalkeeper being world class, and B him saving the penalty)

    An additional question is: If he saves the penalty in a row would you then think he was world class?

    Another additional question is: If he has 10 penalties taken against him, how many would he have to save for you to be 95% confident that he was world class?

    Any help would be great!

    For the later parts of this question you need to be able to claculate the
    probability of a keeper saving N from M penalties given the probability of
    saving a single penalty p.

    The number saved from M has a binomial distribution so:

    P(N,M)=b(N;M,p)

    RonL
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