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Math Help - Composition of independent events

  1. #1
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    Composition of independent events

    You roll a die 3 times.
    (a) What is the probability of getting a total of two 5's from all three rolls of the die?

    (b) What is the probability of getting a total of at least two 5's from all three rolls of the die?

    So for (a), I think of it this way: P(5 5 5') where 5 is the probability of getting a 5 and 5' is the probability of not getting a 5. So:

    P(5 5 5') = (1/6)*(1/6)*(5/6) = 5/216. So my answer for (a) would be 5/216.

    Whats the correct way to think about (b)? Thanks,
    Kim
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  2. #2
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    Quote Originally Posted by Kim Nu View Post
    You roll a die 3 times.
    (a) What is the probability of getting a total of two 5's froorm all three rolls of the die?
    (b) What is the probability of getting a total of at least two 5's from all three rolls of the die?
    You need another factor in the answer for the (a) part to account for position: {3 \choose 2} \left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)

    For (b) you two or three 5's: \sum\limits_{k = 2}^3 {{3 \choose k}\left( {\frac{1}{6}} \right)^k \left( {\frac{5}{6}} \right)^{3 - k} }
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