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Math Help - win win problem

  1. #1
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    win win problem

    Dear Sir,
    I need help some help with the below problem and would appreciate very much if can offer some help.
    thanks
    Kingman

    1) In a match, 2 teams (A and B) will play each other in the best of 3 games. That is, the final team to win 2 games will be the winner. In the first games, both teams have equal chance of winning. In subsequent games, the probability of team A winning team B given that team A won in the previous game is p and the probability of team A winning team B given that team A lost in the previous game is 1/3.

    Find the value of p such that the team A has equal chances of winning and losing the competition.

    Answer(2/3)
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  2. #2
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    Quote Originally Posted by kingman View Post
    Dear Sir,
    I need help some help with the below problem and would appreciate very much if can offer some help.
    thanks
    Kingman

    1) In a match, 2 teams (A and B) will play each other in the best of 3 games. That is, the final team to win 2 games will be the winner. In the first games, both teams have equal chance of winning. In subsequent games, the probability of team A winning team B given that team A won in the previous game is p and the probability of team A winning team B given that team A lost in the previous game is 1/3.

    Find the value of p such that the team A has equal chances of winning and losing the competition.

    Answer(2/3)
    Have you tried this on your own? You can draw a decision tree, maybe known to you as a probability tree. You will need to write an equation and solve for p.
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  3. #3
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    The probability tree would give you all you need and you just start from the beginning and work your way down.
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  4. #4
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    Question this is exactly my difficulty lies

    Dear oregon88,
    Thanks very much for your reply. I have great difficulty in drawing my tree diagram.

    Here is my difficulty:
    A either win or lose and
    B either win or lose but the question only mention winning: from here I am stuck !
    How to draw the tree giving all the outcomes is my problem.
    please help
    thanks

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  5. #5
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    Quote Originally Posted by kingman View Post
    Dear oregon88,
    Thanks very much for your reply. I have great difficulty in drawing my tree diagram.

    Here is my difficulty:
    A either win or lose and
    B either win or lose but the question only mention winning: from here I am stuck !
    How to draw the tree giving all the outcomes is my problem.
    please help
    thanks
    P(win) = 1 - P(lose)
    P(lose) = 1 - P(win)

    This is because the probabilities for all possible outcomes must always add up to 1. (As in, 100%)

    Does that help?
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  6. #6
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    thanks,
    I know this fact but still need to know how the tree diagram look which depicts the win and lose of both A and B.
    This does not look like a typical tree diagram.
    Please help!
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  7. #7
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    Quote Originally Posted by kingman View Post
    thanks,
    I know this fact but still need to know how the tree diagram look which depicts the win and lose of both A and B.
    This does not look like a typical tree diagram.
    Please help!
    Hmm, the diagram is typical enough if you ask me. I don't know if you're used to going up to down, but I generally go left to right. Attached. (It's kind of ugly since it's with MS Paint/mouse.) Overall win for A is marked in green, otherwise blue.
    Attached Thumbnails Attached Thumbnails win win problem-probtreewinwin.png  
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