Interesting GMATFix Problem-51

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

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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Source: Beat The GMAT — Problem Solving | Sat Oct 09, 2010 2:04 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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 Ã— 0.5 Ã— 0.2 = 0.02

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

"¢ Moscow, Paris rain and NY doesn't, probability is = 0.8 Ã— 0.5 Ã— 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]

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

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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Arcane66: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Sat Aug 08, 2009 1:16 pm; Thanked: 2 times

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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