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Math Help - Dice and Doubles

  1. #1
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    Dice and Doubles

    Hey everyone,
    Here's the question:

    a)Two dice are thrown n times in succession. Compute the probability that a double six appears at least once. How large does n have to be for this probabablity to be at least 1/2?

    b)Two dice are thrown n times in succession. Compute the probability that some double(be it 6's or 5's...) appears at least once. How large does n have to be for this probability to be at least 1/2?

    ok, so I know that the probability for double sixes would be 1/6 * 1/6 = 1/36. I definitly don't know how to figure out how many throws you would need for the probability to be 1/2.

    Thanks!
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  2. #2
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    Quote Originally Posted by kelli_rie View Post
    Hey everyone,
    Here's the question:

    a)Two dice are thrown n times in succession. Compute the probability that a double six appears at least once. How large does n have to be for this probabablity to be at least 1/2?

    [snip]
    (a) Let X be the random variable number of double sixes.

    X ~ Binomial(n, p = 1/36).

    (i) \Pr(X \geq 1) = 1 - \Pr(X = 0) = 1 - \left( \frac{35}{36}\right)^n.

    (ii) You require the smallest integer value of n such that \Pr(X \geq 1) \geq \frac{1}{2} \Rightarrow \left( \frac{35}{36}\right)^n \leq \frac{1}{2}.

    Trial and error is as good a way as any for solving for n.
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    Quote Originally Posted by kelli_rie View Post
    [snip]
    b)Two dice are thrown n times in succession. Compute the probability that some double(be it 6's or 5's...) appears at least once. How large does n have to be for this probability to be at least 1/2?

    [snip]
    Let Y be the random variable number of doubles.

    Y ~ Binomial(n, p = .....)

    You should be able to calculate the value of p (the probability of getting a double in a single throw). Now model your solution on the solution to (a).
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