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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
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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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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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

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