It is currently 29 Oct 2020, 15:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2976 [1] , given: 394

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

Question Stats:

64% (01:00) correct 35% (00:47) wrong based on 98 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

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Active Member
Joined: 07 Jan 2018
Posts: 694
Followers: 11

Kudos [?]: 778 [2] , given: 88

Re: The probability of rain is on any given day next week. [#permalink]  07 Aug 2018, 05:09
2
KUDOS
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, $$\frac{(2^7 - 1)}{2^7} = \frac{127}{128}$$
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos

Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2976 [2] , given: 394

Re: The probability of rain is on any given day next week. [#permalink]  09 Aug 2018, 15:09
2
KUDOS
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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager
Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 138 [1] , given: 22

Re: The probability of rain is on any given day next week. [#permalink]  03 Jan 2019, 17:37
1
KUDOS
Set = {x+1, x+2, x+3, …., x+35}

A: The probability for selecting an even number less than median:
The median is (35-1)/2+1 = 18th which is x+18
Numbers before median are: x+1, x+2, …, x+17 there are 17 numbers before median, and as 17 is not even, we don’t know there are either 9 or 8 even numbers.
A would be either 9/35 or 8/35

B: The probability for selecting an odd number greater than median:
The median is (35-1)/2+1 = 18th which is x+18
Numbers after median are: x+19, x+19, x+20, …, x+35, there are 17 numbers after median, we don’t know there are either 9 or 8 even numbers.
B would be either 9/35 or 8/35

We don’t know the first number in the sequence is even or odd, if we knew we were sure what situation would happen.
_________________

Director
Joined: 22 Jun 2019
Posts: 517
Followers: 5

Kudos [?]: 106 [0], given: 161

Re: The probability of rain is on any given day next week. [#permalink]  18 Jul 2019, 03:58
sandy wrote:
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.

It is said that the probability of raining at any given day next week is 1/2. SO why you took 1/2 for no raining day. I'm confused here. please clarify.

_________________

New to the GRE, and GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary

GRE Instructor
Joined: 10 Apr 2015
Posts: 3874
Followers: 159

Kudos [?]: 4678 [1] , given: 70

Re: The probability of rain is on any given day next week. [#permalink]  18 Jul 2019, 06:58
1
KUDOS
Expert's post
huda wrote:

It is said that the probability of raining at any given day next week is 1/2. SO why you took 1/2 for no raining day. I'm confused here. please clarify.

If, for example, P(rain in Monday) = 0.5, then P(NO rain on Monday) = 1 - 0.5 = 0.5

Likewise, if it were the case that P(rain in Monday) = 0.3, then P(NO rain on Monday) = 1 - 0.3 = 0.7, etc.

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Director
Joined: 22 Jun 2019
Posts: 517
Followers: 5

Kudos [?]: 106 [0], given: 161

Re: The probability of rain is on any given day next week. [#permalink]  18 Jul 2019, 07:27
GreenlightTestPrep wrote:
huda wrote:

It is said that the probability of raining at any given day next week is 1/2. SO why you took 1/2 for no raining day. I'm confused here. please clarify.

If, for example, P(rain in Monday) = 0.5, then P(NO rain on Monday) = 1 - 0.5 = 0.5

Likewise, if it were the case that P(rain in Monday) = 0.3, then P(NO rain on Monday) = 1 - 0.3 = 0.7, etc.

Does that help?

Cheers,
Brent

yes, thank you so much.
_________________

New to the GRE, and GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary

Re: The probability of rain is on any given day next week.   [#permalink] 18 Jul 2019, 07:27
Display posts from previous: Sort by