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Difficult Math Problem #74 - Probability

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Problem #74 - Probability

Post Mon Dec 11, 2006 5:53 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the probability of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?

    8/125
    2/25
    5/16
    8/25
    3/4

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    jayofbay Junior | Next Rank: 30 Posts Default Avatar
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    Post Tue Dec 12, 2006 12:11 am
    answer is 5/16

    Choosing 3 days out of 5 is 5C3 = 5!/(3! x 2!) = 10
    3 days of rain = P(A) = 1/2 x 1/2 x 1/2 = 1/8
    and 2 days of no rain is P(B) = (1-1/2)X(1-1/2) = 1/4
    P(A and B) = P(A) X P(B) = 1/32
    So total number of such cases is 10 hence probability is
    10 x 1/32 = 5/16

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Dec 13, 2006 4:24 pm
    OA:

    Use binomial theorem to solve the problem....

    p = 1/2
    q = 1/2
    # of favorable cases = 3 = r
    # of unfavorable cases = 5-3 = 2
    total cases = 5 = n

    P(probability of r out of n) = nCr*p^r*q^(n-r)

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