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Math Help - Binomial Distribution

  1. #1
    Yan
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    Binomial Distribution

    A gambler decides to keep betting on red at roulette, and stop as soon as she has won a total of five bets.

    a) what is the probability that she has to make exactly 8 bets before stopping?

    b) what is the probability that she has to make at least 9 bets?
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    Quote Originally Posted by Yan View Post
    A gambler decides to keep betting on red at roulette, and stop as soon as she has won a total of five bets.

    a) what is the probability that she has to make exactly 8 bets before stopping?

    b) what is the probability that she has to make at least 9 bets?
    First you need to tell me what's the probability of getting red in a single spin of the wheel.
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  3. #3
    Yan
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    i don't know, i only got the problem and i don't know how to do it....
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    Quote Originally Posted by Yan View Post
    i don't know, i only got the problem and i don't know how to do it....
    Then call the value p. You can chase up the value from your instructor.

    Now use the negative binomial distribution: Negative binomial distribution - Wikipedia, the free encyclopedia
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  5. #5
    Yan
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    the percentage of bets on red each time is (1/2)
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    Quote Originally Posted by Yan View Post
    the percentage of bets on red each time is (1/2)
    I'll do it using only the binomial distribution (you might not be familiar with the negative binomial distribution).

    a) You need exactly 2 successes in the first 7 trials and then a succes on the 8th trial.

    Let X ~ Binomial(n = 7, p = 1/2).

    Then Pr(8 trials) = \Pr(X = 2) \cdot \frac{1}{2}.


    b) Pr(9 or more trials) = 1 - Pr(8 or less trials) = 1 - Pr(8 trials) - Pr(7 trials) - ..... - Pr(4 trials) - Pr(3 trials).

    Calculate Pr(7 trials), Pr(6 trials), ...... Pr(3 trials) in a similar way to how Pr(8 trials) was calculated.
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