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Math Help - Probability/Expectation of game

  1. #1
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    Probability/Expectation of game

    Hey guys I'm having a hard time on this problem ... any help would be great!

    In the game of "odd one out" three people each toss a fair coin to see if one of their coins shows a different face from the other two.
    a) After one play, what is the probability of some person being the "odd one out"?
    b Suppose play continues until there is an "odd one out". What is the probability that the duration is r plays?
    c) What is the expected duration of play?
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  2. #2
    MHF Contributor matheagle's Avatar
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    This is a geometric RV.

    q=P(HHH or TTT)=1/4

    So p=3/4 and E(X)=1/p=4/3

    P(game takes r plays)= pq^{r-1}
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