Probability

[800GMAT]

There is a 10% chance that it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest possible probability that it will snow and schools will be closed during the winter?

(A) 55%
(B) 60%
(C) 70%
(D) 72%
(E) 80%


OA: E

need an approach to solve this one...

[camitava]

800GMAT,
10% chance that it won't snow all winter long => 90% chance that it will snow all winter long
20% chance that schools will not be closed all winter long => 80% chance that schools will be closed all winter long
Combining these two statements together, we can get that there is 80% chance that schools will be closed all winter long and it will snow all winter long.
Am I clear 800GMAT?

[samirpandeyit62]

This one seems to be a little weird to me

I agree that the max P that schools will be closed all winter long = 8/10 =80%

but if this is the P i.e the greatest possible probability that it will snow and schools will be closed during the winter.

then it means taking the P that it will snow = 1 i.e maximizing it

now if this corresponds to snow fall on atleast 1 day during winter (question mentions during winter & not all winter)

then the P =1 can be justified but in that case same will be applicable for the schools also so that too must considered as P of schools remaining closed on at least 1 day during winter, this P would be greater than 80%

so IMO the question has some logical flaw.

Any opinions/ corrections appreciated.

[yuri]

aren't we supposed to multiply 9/10 and 8/10 to get 72% of the both being closed/snowing together??

[samirpandeyit62]

Hi Yuri,
I also meant that 72% is the answer which comes out, for E to be correct, the probability of snow should be 1 which produces a conflict here.