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Math Help - Probability of Rain occuring

  1. #1
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    Exclamation Probability of Rain occuring

    If the probability of rain is 60% on each of three consecutive days, find:
    1)the probability that it rains on all three days,
    2)the probability that it rains on exactly two of the three days?
    For number 1 my anwer was .064 and for number 2 my answer was .288, am I correct? If not can you help me please?
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  2. #2
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    Quote Originally Posted by journeygirl280 View Post
    If the probability of rain is 60% on each of three consecutive days, find:
    1)the probability that it rains on all three days,
    2)the probability that it rains on exactly two of the three days?
    For number 1 my anwer was .064 and for number 2 my answer was .288, am I correct? If not can you help me please?
    It would help if you told us why you think these are the answers.

    The number of days out of 3 that is rains in a binomial random variable with
    distribution B(3, 0.6), for which:

    p(n; 3, 0.6) = 3!/(n!(3-n)!) 0.6^n (1-0.6)^{3-n}.

    For (1), n=3, and so:

    p(3; 3, 0.6) = 0.6^3 ~= 0.216.

    For (2), n=2, and so:

    p(2; 3, 0.6) = 3 (0.6^2) (0.4) ~= 0.432

    RonL
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  3. #3
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    Smile Thanks

    Thank you for your help which leads me to another question. What is the relationship between the answers and the binomial expansion of
    (0.4 + 0.6)^3. I know that the binomial expansion equals 1 but how does that relate to the answers you got?
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