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Math Help - Probability Q

  1. #1
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    Probability Q

    Here's a question from my homework that I'm stuck on:
    Gunter tosses a die first, then Vlad. They repeat this until someone tosses a four, which means that person wins. Find the probability that Gunter wins, and the probability that Vlad wins.
    For Gunter to win, wouldn't the probability just be 1/6, and for Vlad, the probability would be 5/6 * 1/6?
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  2. #2
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    Re: Probability Q

    Quote Originally Posted by Otto45 View Post
    Here's a question from my homework that I'm stuck on:
    Gunter tosses a die first, then Vlad. They repeat this until someone tosses a four, which means that person wins. Find the probability that Gunter wins, and the probability that Vlad wins.
    For Gunter to win, wouldn't the probability just be 1/6, and for Vlad, the probability would be 5/6 * 1/6?

    Gunter can win on the first, third, fifth, etc turn.
    The probability that Gunter wins on the ninth toss is {\left( {\frac{5}{6}} \right)^8}\left( {\frac{1}{6}} \right).
    Can you explain why?

    What is this sum \left( {\frac{1}{6}} \right)\sum\limits_{k = 0}^\infty  {{{\left( {\frac{5}{6}} \right)}^{2k}}} =~?

    What does that sum represent?
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