Interesting GMATFix Problem-51

[arora007]

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

[sanju09]

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. [/spoiler]

[arora007]

Congrats Sanju...
I guess I am lucky to have ur 2500 post on my post...
I hope to see a 51 in my Q

[Arcane66]

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.