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Math Help - partition law

  1. #1
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    partition law

    Two basketball players throw a ball into the basket till the first hit.
    The probability for the first player tol hit the target is 5%, but for the second - 15%.
    What is the partition law for the number of attempts both player made.

    thanks for help.
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  2. #2
    MHF Contributor

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    Re: partition law

    Are you asking "how can I look at this problem and immediately know the aswer without doing any calculation?" I have no idea. But sitting down and doing some calculations might well show a pattern.

    The first player will win on the first throw .05 of the time.
    The second player will win on his first throw if the first player misses and he hits: (.95)(.15)
    The first player will win on the second throw if the first player misses on the first try, second player misses, first player hits on second try: [tex](.95)(.85)(.05)
    The second player will win on his second throw if the first player misses, second player misses, first player misses, second player hits: [tex](.95)(.85)(.95)(.15)
    The first player will win on the third throw if they both miss twice and the he hits: (.95)(.85)(95)(.85)(.05)
    The second player will win on the third throwif they bothiss twice, the first player misses, the second player hits: (.95)(.85)(.95)(.85)(.95)(.15)

    So far for the first player we have
    1: .05= ((.95)(.05))^0(.05)
    2: .95(.85)(.05)= ((.95)(.85)^1)(.05)
    3: .95(.85)(.95)(.85)(.05)= ((.95)(.85))^2(.05)
    See a pattern?
    Last edited by HallsofIvy; April 11th 2013 at 12:47 PM.
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  3. #3
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    Re: partition law

    Quote Originally Posted by HallsofIvy View Post
    Are you asking "how can I look at this problem and immediately know the aswer without doing any calculation?" I have no idea. But sitting down and doing some calculations might well show a pattern.

    The first player will win on the first throw .05 of the time.
    The second player will win on his first throw if the first player misses and he hits: (.95)(.15)
    The first player will win on the second throw if the first player misses on the first try, second player misses, first player hits on second try: [tex](.95)(.85)(.05)
    The second player will win on his second throw if the first player misses, second player misses, first player misses, second player hits: [tex](.95)(.85)(.95)(.15)
    The first player will win on the third throw if they both miss twice and the he hits: (.95)(.85)(95)(.85)(.05)
    The second player will win on the third throwif they bothiss twice, the first player misses, the second player hits: (.95)(.85)(.95)(.85)(.95)(.15)

    So far for the first player we have
    1: .05= ((.95)(.05))^0(.05)
    2: .95(.85)(.05)= ((.95)(.85)^1)(.05)
    3: .95(.85)(.95)(.85)(.05)= ((.95)(.85))^2(.05)
    See a pattern?
    Thanks for this.
    But I don't know how to write this as a parition law.
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