It is currently 20 Sep 2017, 06:17

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the probability that it will rain on each of the next 3 days i

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41634

Kudos [?]: 124124 [0], given: 12072

What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 03 Nov 2014, 08:11
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (00:56) correct 36% (00:54) wrong based on 223 sessions

HideShow timer Statistics

Tough and Tricky questions: Probability.



What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period? (Assume that the probability of rain on one day is independent of the probability of rain on any other day).

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Edit: Original question is below:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Edited after Ian Stewart's comment below
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics


Last edited by Bunuel on 14 Aug 2017, 01:06, edited 1 time in total.
Edited.

Kudos [?]: 124124 [0], given: 12072

4 KUDOS received
Intern
Intern
avatar
Joined: 12 May 2013
Posts: 27

Kudos [?]: 54 [4], given: 16

Concentration: Finance, Economics
GMAT 1: 700 Q49 V36
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 03 Nov 2014, 13:50
4
This post received
KUDOS
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

A = rain
B = no rain

What is \(P(A)*P(A)*P(A) = P(A)^3\) ?


(1) The probability of no rain throughout the first two days is 36%.

\(P(B)*P(B) = 0,36\) ---> \(P(B) = 0,6\)

\(P(A) = 1 - P(B) = 1 - 0.6 = 0.4\)

\(P(A)^3 = 0,4^3 = 0,064\)


SUFFICIENT


(2) The probability of rain on the third day is 40%.

\(P(A) = 0,4\)
\(P(A)^3 = 0,4^3 = 0,064\)


SUFFICIENT

Correct answer is D

:-D
_________________

Feel free to message if you have any questions :D

Kudos [?]: 54 [4], given: 16

1 KUDOS received
Intern
Intern
User avatar
Joined: 04 Jul 2014
Posts: 48

Kudos [?]: 36 [1], given: 40

Schools: Smeal" 20
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 05 Nov 2014, 13:20
1
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Probability.



What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.



Raining on any day is an independent event. Lets take the probability of raining on a single day as 1/x. Therefore probability of no rain on that day is [1-1/x] .

what is asked is if 1/x * 1/x * 1/x can be found out

[1] Probability of No rain in the first two days = 36%

i.e [1-1/x] * [1-1/x] = 36% . From this we can find [1/x]^3. Therefore sufficient.

[2] Probability of rain on third day is 40%.

1/x is 40% . Probability is same for all the days. So [1/x]^3 can be found out. Therefore sufficient.

Hence D.

-------------

Please give kudos if this helps.

Kudos [?]: 36 [1], given: 40

Manager
Manager
avatar
Joined: 12 Sep 2014
Posts: 168

Kudos [?]: 81 [0], given: 103

Concentration: Strategy, Leadership
GMAT 1: 740 Q49 V41
GPA: 3.94
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 07 Nov 2014, 09:00
Both statements are essentially saying that the probability of rain on any given day is 40%. Since the probability that it will rain on any given day is constant, both statements are sufficient on their own.

D

Kudos [?]: 81 [0], given: 103

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17568

Kudos [?]: 270 [0], given: 0

Premium Member
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 06 Sep 2016, 21:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Manager
Manager
avatar
S
Joined: 06 Jul 2014
Posts: 101

Kudos [?]: 34 [0], given: 155

Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 640 Q48 V30
GMAT ToolKit User Reviews Badge
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 13 Aug 2017, 12:53
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Kudos [?]: 34 [0], given: 155

Expert Post
2 KUDOS received
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1341

Kudos [?]: 1908 [2], given: 6

Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 13 Aug 2017, 16:27
2
This post received
KUDOS
Expert's post
Bounce1987 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.


If the probability it rains on one day is p, then the probability it does not rain on one day is 1-p. The probability it does not rain on the first two days is thus (1 - p)*(1 - p). So using Statement 1, we know:

(1 - p)^2 = 36/100

Take the square root, and 1-p = 6/10, so p = 4/10. So Statement 1 is equivalent to Statement 2 - both tell us that the probability of rain on any day is 0.4. That means the probability it rains on all three days is 0.4*0.4*0.4, so we can answer the question. So the answer is D.

I'm assuming above that the probability of rain on one day is independent of the probability of rain on any other day. You can only use the multiplication rules I used above when that's true. That's something that almost certainly is not true in real life (if it rains one day, that probably makes rain more likely the next day, which means they're not independent), so any question like this really needs to tell you the events are independent, because it's not a natural thing to assume. If you don't know the events are independent, you can't solve this. Where is the question from?
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1908 [2], given: 6

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41634

Kudos [?]: 124124 [0], given: 12072

Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 14 Aug 2017, 01:07
Bounce1987 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.


Merging topics. Please search before posting. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124124 [0], given: 12072

Manager
Manager
avatar
G
Joined: 27 Jan 2016
Posts: 131

Kudos [?]: 60 [0], given: 61

Schools: ISB '18
CAT Tests
Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

Show Tags

New post 14 Aug 2017, 01:16
Stmnt 1) P(No Rain) x P(No Rain) = 36/100

So, P(No Rain)=6/10 -> P(Rain) = 4/10

Hence P(Rain)xP(Rain)xP(Rain) = (4/10)^3

Stmnt 2) P(Rain) = 4/10

Hence P(Rain)xP(Rain)xP(Rain) = (4/10)^3

Answer D

Kudos [?]: 60 [0], given: 61

Re: What is the probability that it will rain on each of the next 3 days i   [#permalink] 14 Aug 2017, 01:16
    Similar topics Author Replies Last post
Similar
Topics:
8 EXPERTS_POSTS_IN_THIS_TOPIC Steve spent a total of $36 on transportation for 3 days. What was his alphonsa 2 05 May 2016, 14:27
4 EXPERTS_POSTS_IN_THIS_TOPIC What is the probability of (x+3)(x+10) being div by 6? chetan2u 2 25 Apr 2016, 22:55
2 EXPERTS_POSTS_IN_THIS_TOPIC If the probability of snow is the same every day this week, what is th Bunuel 2 05 Aug 2016, 05:24
EXPERTS_POSTS_IN_THIS_TOPIC Next week, each of the summer interns will be given either 2 or 3 proj Bunuel 2 30 May 2016, 21:43
2 What is the probability that it will rain tomorrow ? aashu4uiit 7 04 Aug 2016, 08:00
Display posts from previous: Sort by

What is the probability that it will rain on each of the next 3 days i

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.