Results 1 to 6 of 6

Math Help - probability

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    43

    probability

    Sasha and Pedro meet every Tuesday for a game of backgammon. They find that after winning a game, sasha has a 65% probability of winning the next game. Similarly, Pedro has a 60% probability of winning after he has won a game. Pedro won the game last week.
    QUESTION: a) If Pedro and Sasha play 100 games, how many games is each player likely to win?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ives View Post
    Sasha and Pedro meet every Tuesday for a game of backgammon. They find that after winning a game, sasha has a 65% probability of winning the next game. Similarly, Pedro has a 60% probability of winning after he has won a game. Pedro won the game last week.
    QUESTION: a) If Pedro and Sasha play 100 games, how many games is each player likely to win?
    Are you familiar with Markov chains, transition matrices, initial state etc.?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    43
    no idea about the term what u said..........
    sorry....
    thanks for help
    Follow Math Help Forum on Facebook and Google+

  4. #4
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by ives View Post
    no idea about the term what u said..........
    sorry....
    thanks for help
    Your question cannot simply be answered by using distributions such as Binomial or Poisson. You need to have the knowledge of a 2 x 2 Markov Chain, so that you can analyze the 100th transition/state.

    All Markov chains are mixed probability distributions based on if a given event(s) happens.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2008
    Posts
    43
    haha however, my exam has passed, so easy
    thanks a lot for ur helps
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ives View Post
    Sasha and Pedro meet every Tuesday for a game of backgammon. They find that after winning a game, sasha has a 65% probability of winning the next game. Similarly, Pedro has a 60% probability of winning after he has won a game. Pedro won the game last week.
    QUESTION: a) If Pedro and Sasha play 100 games, how many games is each player likely to win?
    While this is an example of a Markov chain you don't need to know about Markov chains to solve it.

    Suppose that in the long run S wins a proportion s of the games and P wins a proportion p of the games, then s+p=1.

    Now suppose a game is played. the probability that S won is s and that P won is (1-s) , so the probability that S wins the following game is:

    s_1=s \times 0.65 + (1-s) \times 0.35

    But if we have a limiting probablity s_1=s, so we have:

    s=s \times 0.65 + (1-s) \times 0.35

    so:

    s=0.5

    Now in a run 100 of games the distribution of wins will be affected by the initial conditions, and we know nothing of the win probabilities in the abscence of a previous result, but to a hand waveing approximation we can say that each player will have won about half of the games.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  2. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  3. fundamental in probability & convergence with probability 1
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 23rd 2010, 09:58 AM
  4. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  5. Replies: 3
    Last Post: December 15th 2009, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum