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Math Help - probability dice problem

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    probability dice problem

    A fair die is rolled six times. The probability of rolling more than 4 at least five times is

    (a) 2/729 b) 3/729 c) 12/729 d) 13/729 (e) none of the above
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    Whats the probability of rolling five 4's? Of six?
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  3. #3
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    Hello sri340
    Quote Originally Posted by sri340 View Post
    A fair die is rolled six times. The probability of rolling more than 4 at least five times is

    (a) 2/729 b) 3/729 c) 12/729 d) 13/729 (e) none of the above
    The die shows more than 4 if it lands showing 5 or 6. We'll call this a 'success'. So the probability of a success on a single roll is \frac26=\frac13. The probability of a 'failure' on a single roll is \frac23.

    We want the probability that when the die is rolled six times we get 5 sucesses, p(5), or 6 successes, p(6).

    For p(5) we want 5 successes and 1 failure. The failure can occur on any one of the 6 rolls. So p(5) = 6 \times \left(\frac13\right)^5\times \left(\frac23\right) = \frac{12}{729}.

    For p(6) we must have all 6 successes. So p(6) = \left(\frac13\right)^6 = \frac{1}{729}.

    Therefore the probability that one or other of these events occurs is \frac{12}{729}+\frac{1}{729}=\frac{13}{729}

    Grandad
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