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Math Help - rolling two dices probability problem

  1. #1
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    Exclamation rolling two dices probability problem

    anybody can help with the next problem:?
    A game begins by choosing between dice A and B is some manner such that the probability that A is selected is 'p'. The die thus selected is then tossed until a white face appears, at which time the game is conluded. Die a has 4 red and 2 white faces. Die B has 2 red and 4 white faces. After playing this game a great many times, it is observed that the probability that a game is concluded in exactly three tosses of the selected die is 7/81. Determine the value of p.

    cheers...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rbenito View Post
    anybody can help with the next problem:?
    A game begins by choosing between dice A and B is some manner such that the probability that A is selected is 'p'. The die thus selected is then tossed until a white face appears, at which time the game is conluded. Die a has 4 red and 2 white faces. Die B has 2 red and 4 white faces. After playing this game a great many times, it is observed that the probability that a game is concluded in exactly three tosses of the selected die is 7/81. Determine the value of p.

    cheers...
    Suppose die A is selected, then the probability that the game ends in exactly three tosses is (4/6)(4/6)(2/6)

    Suppose die B is selected, then the probability that the game ends in exactly three tosses is (2/6)(2/6)(4/6)

    Thus if die A is selected with probability p the probability that the game ends in exactly 3 moves is:

    p [ (4/6)(4/6)(2/6) ] + (1-p) [ (2/6)(2/6)(4/6) ] = 7/81

    Now solve for p.

    RonL
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  3. #3
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    Thank you very much

    The solution seems very simple, thank you.
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