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# Probabilty of rain

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Intern
Joined: 09 Feb 2006
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Probabilty of rain [#permalink]  13 Feb 2006, 07:03
Hello everyone,

I just registered on this site a couple of days back and this is my first post I'm just glad to have found this forum. I plan to take my GMAT sometime in June.

OK getting to the point. Here is the question: -

The probability that it will rain on a day is 0.5. What is the probability that it will rain on exactly three days out of a five day working week.
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Intern
Joined: 09 Feb 2006
Posts: 21
Location: Raleigh, NC
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I'm not sure if I have solved it correctly, but here is how I approached it.

-> Number of ways to pick exactly three days from a 5 day week = 10
-> P(Rains) = P(Does not Rain) = 0.5

-> Reqd. Probability 10 * ( [P(Rains)]^3 ) * ( [P(Doesn't Rain)]^2 )

-> 10/(32)

-> 5/16

I dont know if my approach is right. Any comments?
Director
Joined: 13 Nov 2003
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think that your approach is correct
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probability [#permalink]  19 Feb 2006, 10:09
Why should u multiply this answer by 10? I am not following...
Intern
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your answer seems right. Do you have any OA and explanation for this question?
Director
Joined: 05 Feb 2006
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Total outcomes are equal to: 5 days, each day has an equal possibility to be a rain day or not so 2*2*2*2*2=32

The possibility that 3 days out of 5 will be rainy is: 5C3=10

So total possibility=10/32=5/16
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P = (0.5)^3 (0.5)^2 = (0.5)^5 = 0.3125
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