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Math Help - Probability/Die question.

  1. #1
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    [Solved]Probability/Die question.

    In rolling two fair dice simultaneously, the probability of rolling a 7 or 11 is 2/9. What is the approximate probability of rolling a 7 or 11 two or more times in ten rolls of two dice?

    Need some direction I really don't know where to start with this one.
    Last edited by jmsal; May 28th 2009 at 04:07 PM. Reason: solved
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  2. #2
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    The probability of rolling 7 or 11 2 or more times in 10 rolls P (7\vee 11\geq 2) is the same as 1-probability of rolling 7 or 11 less than 2 times in 10 rolls.

    This is equal to 1-(probability of rolling 7 or 11 zero times +probability of rolling 7 or 11 one time)


    The binomial distribution is the best tool to compute the probability of rolling 7 or 11 x times

    Probabilitiy of rolling a 7 or 11 one time out of 10 rolls= \binom{10}{1}\left(\frac{2}{9}\right)^1\left(1-\frac{2}{9}\right)^9=\binom{10}{1}\frac{2}{9}\left  (\frac{7}{9}\right)^9

    and the probability of rolling a 7 or 11 zero times out of 10 rolls= \binom{10}{0}\left(\frac{2}{9}\right)^0\left(1-\frac{2}{9}\right)^{10}=\binom{10}{0}\left(\frac{7  }{9}\right)^{10}

    Search google for the binomial distribution if you're still confused
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  3. #3
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    Thank you so much. I forgot to mention that this is a multiple choice:
    A:0.08 B:0.23 C:.30 D:0.69 E:.77.

    Going from youre calculations the best answer is A:0.08
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  4. #4
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    no the best answer is D

    add the two calculations, subtract that from one, and you get .687
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