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Math Help - probability of winning a no-ad tennis game

  1. #1
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    probability of winning a no-ad tennis game

    if the probability of winning a point is p, what is the probability of winning a tennis game under the "no-ad" scoring? (The first player who wins four points wins the game.) Thanks~
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  2. #2
    MHF Contributor matheagle's Avatar
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    Does that mean you can win the game 4-3?
    I once solved a math monthly that asked to maximize teams winning a 7 games series.
    This is the same idea. First to four wins.
    Then I did calculus to show a max wrt p.
    You just need to go through the possibilities.

    P({\rm win\; in\; 4})=P(WWWW)=p^4

    P({\rm win\; in\; 5})=4P(LWWWW)=4qp^4
    since the loss can come in any game EXCEPT the fifth game (geometric)

    P({\rm win\; in\; 6})=10P(LLWWWW)=10q^2p^4
    since the loss can come in any game EXCEPT the sixth game (neg binomial)

    we need that 10={5\choose 3} here

    P({\rm win\; in\; 7})=20P(LLLWWWW)=20q^3p^4
    since the loss can come in any game EXCEPT the sixth game (neg binomial)

    we need that 20={6\choose 3} as a coefficient in this one.

    Now, add these, since they are mutually exclusive.
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  3. #3
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    thank you~

    I think your answer is the right one~
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  4. #4
    MHF Contributor matheagle's Avatar
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    was there a contest here?
    Last edited by matheagle; August 30th 2009 at 10:32 PM.
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