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# What is the probability that it will rain on each of the

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What is the probability that it will rain on each of the [#permalink]  23 Nov 2005, 06:44
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What is the probability that it will rain on each of the next 3 days if the probability of rain on any single day is the same in that period?

1. The probability of no rain throughout the fist two days is 36%
2. The probability of rain on the 3rd day is 40%
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Re: DS PGMAT (probability of rain) [#permalink]  23 Nov 2005, 06:51
GMATT73 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of rain on any single day is the same in that period?

1. The probability of no rain throughout the fist two days is 36%
2. The probability of rain on the 3rd day is 40%

I would go with D

1. lets say the prob it does not rains on a day is - 1/x
then 1/(x^2) =36/100. so we can sove for x and find the prob it rains on a day (1 - 1/x)---> sufficient

2. Since the prob is same one each of the 3 days we can find the prob that it rains on each of the next 3 days ---> sufficient
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B)...1) is out b/c 36% is the prob for no rain and 64% ist the prob for at least 1 rainy day. so we cannot calc the prob for 2 days of rain. => insuff
2) is ok
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Current Student
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Good work believe. This is an upper bin problem and the OA is D.
VP
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Matt, could you post the OE? Thanks
VP
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christoph wrote:
B)...1) is out b/c 36% is the prob for no rain and 64% ist the prob for at least 1 rainy day. so we cannot calc the prob for 2 days of rain. => insuff
2) is ok

D)...

1) 36% when its no rain on both days => 6/10 prob that its not raining on 1 day and 4/10 prob that its raining. so (6/10)^3 thats its raining on exactly 3 days. => suff

2) suff
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TeHCM wrote:
Matt, could you post the OE? Thanks
from i, the prob that it will rain on ach of first and second day is = prob (rain on 1st day) prob (rain on 2nd day) = sqrt(0.36) = 0.4 or 40%. suff.

from ii, if the prob that it rains on third day is 40%, the prob of raining on 1st and 2nd day is also 40%. suff.
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i did it in a different way.

it is a binomial distribution.

so let probability of rain on any single day is x and probability of not rainint is 1-x.

so from statement 1
we get, The probability of no rain throughout the fist two days is 36%
that means nP0 = (1-x)^2 = .36
so, 1-x = .6 so x = .4

therefore probability that it will rain on each of the next 3 days = x^3= .4^3 = .064
so it is suff...

from statement 2) we get The probability of rain on the 3rd day is 40%
that means 3c1 * x. ((1-x)^2 = .4

or, x. (1-x) ^2= .4/3
we can solve for x from here as well and find what is x^3.
so this one is also suff....

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hey ya......

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Re: DS PGMAT (probability of rain) [#permalink]  24 Nov 2005, 03:55
GMATT73 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of rain on any single day is the same in that period?

1. The probability of no rain throughout the fist two days is 36%
2. The probability of rain on the 3rd day is 40%

I agree its D. My working is same as many others here.
Re: DS PGMAT (probability of rain)   [#permalink] 24 Nov 2005, 03:55
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