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Math Help - Roulette

  1. #1
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    Roulette

    A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets  \$1 on red. If red appears (which has probability  \frac{18}{38} ), then the gambler should take her  \$1 profit and quit. If the gamblers loses the bet (which has probability  \frac{20}{38} of occurring), she should make additional  \$1 bets on red on each of the next new spins of the roulette wheel and then quit. Let  X denote the gambler's winnings when she quits.

    (a) Find  P(X>0) .
    (b) Is this a winning strategy?
    (c) Find  E[X] .

    For (a)  P(X>0) = 1 - P(X \leq 0) . This is the easy way to compute it?
    (b) What is the definition of a winning strategy?
    (c) E[X] = \sum x \cdot p(x)
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  2. #2
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    Quote Originally Posted by lord12 View Post
    A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets  \$1 on red. If red appears (which has probability  \frac{18}{38} ), then the gambler should take her  \$1 profit and quit. If the gamblers loses the bet (which has probability  \frac{20}{38} of occurring),

    she should make additional  \$1 bets on red on each of the next new spins of the roulette wheel and then quit. Mr F asks: What does this mean? Do you mean on the next spin, the next two spins, .....??

    Let  X denote the gambler's winnings when she quits.

    (a) Find  P(X>0) .
    (b) Is this a winning strategy?
    (c) Find  E[X] .

    For (a)  P(X>0) = 1 - P(X \leq 0) . This is the easy way to compute it? Mr F says: It's one way of doing it, I suppose. But it would help to know the answer to my above question.
    (b) What is the definition of a winning strategy? Mr F says: E[X] > 0.
    (c) E[X] = \sum x \cdot p(x) Mr F asks: And your question is ....?
    ..
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  3. #3
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    next two spins.
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  4. #4
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    Quote Originally Posted by lord12 View Post
    next two spins.
    Then the only possible value of X that's greater than zero is X = 1. This occurs for either LWW or W. So it's not difficult to calculate Pr(X = 1) ....

    The other possible values of X are:

    X = -3 which occurs for LLL

    X = -1 which occurs for LWL or LLW.

    So it's not difficult to calculate Pr(X = -3) and Pr(X = -1).
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