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Interesting GMATFix Problem-51

by arora007 » Sat Oct 09, 2010 2:04 am
On Monday, the probability of rain in NY is 20% and is Paris is 50% and in Moscow is 80%. If these probabilities are independent, what is the probability that it rains on monday at exactly 2 of these 3 locations?
A)1/50
B)8/25
C)2/5
D)21/50
E)1/2
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by sanju09 » Sat Oct 09, 2010 2:22 am
arora007 wrote:On Monday, the probability of rain in NY is 20% and is Paris is 50% and in Moscow is 80%. If these probabilities are independent, what is the probability that it rains on monday at exactly 2 of these 3 locations?
A)1/50
B)8/25
C)2/5
D)21/50
E)1/2

There are only three ways to have rain at exactly 2 of these 3 locations, and those are:

"¢ NY, Paris rain and Moscow doesn't, probability is = 0.2 × 0.5 × 0.2 = 0.02

"¢ NY, Moscow rain and Paris doesn't, probability is = 0.2 × 0.8 × 0.5 = 0.08

"¢ Moscow, Paris rain and NY doesn't, probability is = 0.8 × 0.5 × 0.8 = 0.32


Total probability = 0.02 + 0.08 + 0.32 = 0.42 = [spoiler]21/50


D, and this is my 2500th post to the forum.:wink: [/spoiler]
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by arora007 » Sat Oct 09, 2010 11:16 am
Congrats Sanju...
I guess I am lucky to have ur 2500 post on my post...
I hope to see a 51 in my Q :)
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by Arcane66 » Sat Oct 09, 2010 12:51 pm
I also got D but it took a bit of thinking. I separated it into three possibilities. Rain in: 1. NY & P but not M. 2. NY & M but not P. 3. M & P but not NY. If you multiply by using the probability that the first two happen times the probability that the third rain doesn't happen, then you will get 21/50 once you total up the probabilities.
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