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Math Help - Rolling 3 dice

  1. #1
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    Rolling 3 dice

    Hi,

    I have the following question to answer:

    "Three fair dice are rolled. What is the probability of at least one of the dice coming up a four, five or a six?"

    I calculated it the following way:

    P(not 4 or 5 or 6 coming up on 1 dice) = 3/6 = 1/2

    for 3 dice = 1/2 * 1/2 * 1/2 = 1/8

    P(4 or 5 or 6 coming up on any of 3 dice) = 1 - P(not 4 or 5 or 6 on any of 3 dice) = 1 - 1/8 = 7/8

    Is this approach correct?

    Can this also be calculated with the binomial distribution? Could you please give a solution to that?

    Thanks.
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  2. #2
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    Quote Originally Posted by sanv View Post
    "Three fair dice are rolled. What is the probability of at least one of the dice coming up a four, five or a six?"
    P(not 4 or 5 or 6 coming up on 1 dice) = 3/6 = 1/2
    for 3 dice = 1/2 * 1/2 * 1/2 = 1/8
    P(4 or 5 or 6 coming up on any of 3 dice) = 1 - P(not 4 or 5 or 6 on any of 3 dice) = 1 - 1/8 = 7/8

    Can this also be calculated with the binomial distribution? Could you please give a solution to that?
    Yes, that approach is correct.

    For the binomial distribution: \sum\limits_{k = 1}^3 {\binom{3}{k}\frac{1}{{2^3 }}}
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