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# The probability of rain is on any given day next week.

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [1] , given: 375

The probability of rain is on any given day next week. [#permalink]  05 Aug 2018, 14:44
1
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Expert's post
00:00

Question Stats:

58% (00:45) correct 41% (00:55) wrong based on 17 sessions
The probability of rain is $$\frac{1}{2}$$ on any given day next week.

 Quantity A Quantity B The probability that it rains on at least one of the 7 days next week $$\frac{127}{128}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Director
Joined: 07 Jan 2018
Posts: 538
Followers: 4

Kudos [?]: 464 [1] , given: 82

Re: The probability of rain is on any given day next week. [#permalink]  07 Aug 2018, 05:09
1
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The probability that it rains on one of 7 days = 1-probability that it does not rain on any of the 7 days.
probability for not raining on any of the 7 days = $$(1/2)^7 = \frac{1}{2^7}$$
ans = $$1 - \frac{1}{2^7}$$
or, $$\frac{(2^7 - 1)}{2^7} = \frac{127}{128}$$
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: The probability of rain is on any given day next week. [#permalink]  09 Aug 2018, 15:09
Expert's post
Explanation

Since Quantity A is an “at least” problem, use the 1 – x shortcut. Rather than calculate the probability of rain on exactly 1 day next week, and then the probability of rain on exactly 2 days next week, and so on (after which you would still have to add all of the probabilities together!), instead calculate the probability of no rain at all on any day, and then subtract that number from 1.

That will give the combined probabilities for any scenarios that include rain on at least 1 day. Probability of NO rain for any of the 7 days =$$\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{128}$$

Subtract this probability from 1: $$1-\frac{1}{128}=\frac{127}{128}$$.

Quantities A and B are equal.
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Sandy
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Re: The probability of rain is on any given day next week.   [#permalink] 09 Aug 2018, 15:09
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