Results 1 to 3 of 3

Math Help - Probability of Winning Tennis Match

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    144

    Question Probability of Winning Tennis Match

    See figure attached below for the question.

    I was struggling with part a).

    Is there a systematic way of solving for the sample space in this question? (I'm having a hard time determining whether I've truly written down every permutation of winning)

    The outcomes that only last 3 or 4 sets it is still fairly clear whether you've obtained all possible outcomes or not, but for the outcomes that require 5 sets I find myself racking my brain to determine whether or not I've actually listed all the possible outcomes.

    Is there a way to systematically determine this? For example, if I knew from the beginning that there would be 20 samples in my sample space when I have listed say 18, I would know that I am still missing 2 possible samples.

    The only way I could think of simplifying things when generating this sample space is to create a sample space that contains all the games where one particular player ones. Then for the total sample space I would simply invert all the entries so that all the games that the other player could have one are covered as well.

    Any ideas?
    Attached Thumbnails Attached Thumbnails Probability of Winning Tennis Match-statten.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,038
    Thanks
    1675

    Re: Probability of Winning Tennis Match

    Writing "F" for "Federer wins the set" and "R" for "Roddick wins the set" we can have
    "RRR" (Roddick wins in three straight sets)
    "FFF" (Federer wins in three straight sets)
    "RFFF"
    "FRFF"
    "FFRF"
    (But NOT "FFFR" since that would end at "FFF".
    "FRRR"
    "RFRR"
    "RRFR"

    "RRFFF" etc (there are 5!/(2!3!)= 10 ways to order 2 Rs and 3 Fs but we do NOT include FFFRR or FFRFR, etc. There are 4!/3!= 4 ways to get 3Fs in the first four sets so we subtract 10- 4= 6.)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    144

    Re: Probability of Winning Tennis Match

    Quote Originally Posted by HallsofIvy View Post
    Writing "F" for "Federer wins the set" and "R" for "Roddick wins the set" we can have
    "RRR" (Roddick wins in three straight sets)
    "FFF" (Federer wins in three straight sets)
    "RFFF"
    "FRFF"
    "FFRF"
    (But NOT "FFFR" since that would end at "FFF".
    "FRRR"
    "RFRR"
    "RRFR"

    "RRFFF" etc (there are 5!/(2!3!)= 10 ways to order 2 Rs and 3 Fs but we do NOT include FFFRR or FFRFR, etc. There are 4!/3!= 4 ways to get 3Fs in the first four sets so we subtract 10- 4= 6.)
    How did you obtain these numbers,

    \frac{5!}{2!3!}

    Can you generalize it somehow so I know how you are getting those numbers?

    For example,

    \frac{\text{(Number of sets)!}}{(Number of F Wins)!(Number of R Wins)!}

    That formula seems to work for all cases, correct?

    Of course, you would need to remove the cases such as,

    FFFRR and FFRFR as you've mentioned.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability of winning exactly one...
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: October 11th 2010, 03:17 PM
  2. Simple probability question on tennis tournament!
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 9th 2010, 11:35 PM
  3. Theorem tennis match!
    Posted in the Math Challenge Problems Forum
    Replies: 11
    Last Post: June 28th 2010, 10:05 AM
  4. probability of winning a no-ad tennis game
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: August 30th 2009, 09:11 PM
  5. Tennis probability
    Posted in the Statistics Forum
    Replies: 2
    Last Post: April 14th 2009, 09:10 PM

Search Tags


/mathhelpforum @mathhelpforum