GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 10 Dec 2018, 12:38

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

There is a 10% chance that it won't snow all winter long

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

Hide Tags

Manager
Manager
avatar
Joined: 06 Feb 2013
Posts: 53
There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 03 Sep 2013, 22:13
3
26
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (01:43) correct 54% (01:24) wrong based on 500 sessions

HideShow timer Statistics

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%

I have seen several explanations on this one and I cannot understand the point of intersection I guess...Has anyone seen similar problems they saw here (specifically with given probabilities) or perhaps I am looking for a parallel (gumballs, etc) to this problem.

There is one rule on dependent probability P(A) + P(B) - P(AB) but clearly this is not the case here. The dice are independent. With colored balls, we could calculate what happens after the balls taken away (when they are not replaced) and it makes sense. With this type of problem, I do not know what to precisely think of dependent probability :( And what is up with solving probability with overlapping sets or the matrix?

And what exactly happens when we multiply 90% and 80% conceptually? I mean what does that presume and why it is not correct? Basically, a thorough breakdown of this problem would be very helpful.

Please remember that I have seen other explanations, and my questions are based on them. Probably the best of them are:
"The greatest possible probability will occur when b is dependent on a. Thus it will be their intersection set. Hence answer = 0.8"

"They're asking for the greatest possible probability. This will occur if whenever it snows, schools close. This is a causation problem. That means schools will close only if it snows, but not all the time it snows. So you don't have to multiply .9*.8, because each time .8 occurs, .9 will be in effect as well."

I do not understand exactly what they mean...Anyway, I hope you see where I am aiming.

_________________

There are times when I do not mind kudos...I do enjoy giving some for help

Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 06 Sep 2013, 22:27
7
1
obs23 wrote:
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%

I have seen several explanations on this one and I cannot understand the point of intersection I guess...Has anyone seen similar problems they saw here (specifically with given probabilities) or perhaps I am looking for a parallel (gumballs, etc) to this problem.

There is one rule on dependent probability P(A) + P(B) - P(AB) but clearly this is not the case here. The dice are independent. With colored balls, we could calculate what happens after the balls taken away (when they are not replaced) and it makes sense. With this type of problem, I do not know what to precisely think of dependent probability :( And what is up with solving probability with overlapping sets or the matrix?

And what exactly happens when we multiply 90% and 80% conceptually? I mean what does that presume and why it is not correct? Basically, a thorough breakdown of this problem would be very helpful.

Please remember that I have seen other explanations, and my questions are based on them. Probably the best of them are:
"The greatest possible probability will occur when b is dependent on a. Thus it will be their intersection set. Hence answer = 0.8"

"They're asking for the greatest possible probability. This will occur if whenever it snows, schools close. This is a causation problem. That means schools will close only if it snows, but not all the time it snows. So you don't have to multiply .9*.8, because each time .8 occurs, .9 will be in effect as well."

I do not understand exactly what they mean...Anyway, I hope you see where I am aiming.


Ok, let's try to understand the question stem:

There is a 10% chance that it won't snow all winter long. (by the way, there is some ambiguity in this statement)
implies there is a 90% chance that it will snow all winter long i.e. 9 out of 10 winters it will snow all winter long.

There is a 20% chance that schools will not be closed all winter long.
implies there is an 80% chance that schools will be closed all winter long i.e. 8 out of 10 winters school will be closed all winter long.

What is the greatest possible probability that it will snow and schools will be closed during the winter?
Attachment:
Ques3.jpg
Ques3.jpg [ 9.22 KiB | Viewed 7910 times ]


What is the greatest possible overlap between the two? The 8 winters when the school is closed, it should snow all winter long too. That's when the overlap will be maximum. So probability is 0.8
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 155
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 04 Sep 2013, 22:18
11
4
Easily solved with a small table

Here we can infer the values in blue.

So the question asks us what is the maximum for which both C and S are satisfied. The maximum possible value for S is already 80%. For S is 90%. So the maximum for both is 80% (since anything more will no satisfy C i.e. more than 80%).

Hope it helps
Attachments

Untitled.png
Untitled.png [ 3.22 KiB | Viewed 8072 times ]

General Discussion
Intern
Intern
avatar
Joined: 07 Jan 2013
Posts: 36
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Reviews Badge
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 04 Sep 2013, 20:53
3
hi obs,

there are 2 events
1) p(A) (probability it will snow all longer)=0.1
2) p(B)(probability the school will remain close all winter longer)= 1- 0.2 = 0.8

now if you go by rule for joint sets p(A u B) = p(A)+p(B) - p(AandB)
therefore p(AandB)= 0.1 + 0.8 - p(A u B)

now you can just think that p(AandB) could only be max when B is subset of A thereby P(A u B) would be 0.1

hence max p(AandB) would be 0.8,

I hope i made sense
_________________

Help with Kudos if I add to your knowledge realm.

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 630
Location: India
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 05 Sep 2013, 00:30
3
2
obs23 wrote:
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%

I have seen several explanations on this one and I cannot understand the point of intersection I guess...Has anyone seen similar problems they saw here (specifically with given probabilities) or perhaps I am looking for a parallel (gumballs, etc) to this problem.

There is one rule on dependent probability P(A) + P(B) - P(AB) but clearly this is not the case here. The dice are independent. With colored balls, we could calculate what happens after the balls taken away (when they are not replaced) and it makes sense. With this type of problem, I do not know what to precisely think of dependent probability :( And what is up with solving probability with overlapping sets or the matrix?

And what exactly happens when we multiply 90% and 80% conceptually? I mean what does that presume and why it is not correct? Basically, a thorough breakdown of this problem would be very helpful.

Please remember that I have seen other explanations, and my questions are based on them. Probably the best of them are:
"The greatest possible probability will occur when b is dependent on a. Thus it will be their intersection set. Hence answer = 0.8"

"They're asking for the greatest possible probability. This will occur if whenever it snows, schools close. This is a causation problem. That means schools will close only if it snows, but not all the time it snows. So you don't have to multiply .9*.8, because each time .8 occurs, .9 will be in effect as well."

I do not understand exactly what they mean...Anyway, I hope you see where I am aiming.


We have p (A n B) = p(A) + p(B) - p(A u B)

p(A) is the probability that it will snow
p(B) is the probability that the schools will close

p(A n B) will be maximum when p(A u B) is minimum but p(A u B) cannot be less than the higher of the p(A) and p(B) i.e, cannot be less than 0.9.

In the above case B is totally dependent on A. i.,e schools close whenever and only when it snows. So the p(AUB) effectively becomes p(A).

The answer is p(A n B) = 0.9+0.8-0.9= 0.8

In other words the greatest probability is the probability of B.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Manager
Manager
avatar
Joined: 06 Feb 2013
Posts: 53
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 05 Sep 2013, 05:03
1
Helpful guys. Appreciate your efforts. Sravna just to clarify:

We have p (A n B) = p(A) + p(B) - p(A u B)

p(A) is the probability that it will snow
p(B) is the probability that the schools will close

Quote:
p(A n B) will be maximum when p(A u B) is minimum
You mean when p(A u B) maximized, don't you?

In other words, the P(ANB) is maximized when P(AORB) is maximized and this maximization happens only when B is completely dependent on A, becoming A and P(AORB)=P(B). Seem to make sense now. Hope I won't be trapped next time.
_________________

There are times when I do not mind kudos...I do enjoy giving some for help

Manager
Manager
avatar
Joined: 06 Feb 2013
Posts: 53
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 05 Sep 2013, 05:09
adg142000 wrote:
hi obs,

there are 2 events
1) p(A) (probability it will snow all longer)=0.1
2) p(B)(probability the school will remain close all winter longer)= 1- 0.2 = 0.8

now if you go by rule for joint sets p(A u B) = p(A)+p(B) - p(AandB)
therefore p(AandB)= 0.1 + 0.8 - p(A u B)

now you can just think that p(AandB) could only be max when B is subset of A thereby P(A u B) would be 0.1

hence max p(AandB) would be 0.8,

I hope i made sense


It looks like you came from another angle, but it seems to me there are some mix ups. P(A) - will not snow all winter long? Anyhow, was wondering if what you meant was similar to what Sravna was saying? Thanks.
_________________

There are times when I do not mind kudos...I do enjoy giving some for help

Intern
Intern
avatar
Joined: 07 Jan 2013
Posts: 36
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Reviews Badge
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 05 Sep 2013, 05:32
obs23 wrote:
adg142000 wrote:
hi obs,

there are 2 events
1) p(A) (probability it will snow all longer)=0.1
2) p(B)(probability the school will remain close all winter longer)= 1- 0.2 = 0.8

now if you go by rule for joint sets p(A u B) = p(A)+p(B) - p(AandB)
therefore p(AandB)= 0.1 + 0.8 - p(A u B)

now you can just think that p(AandB) could only be max when B is subset of A thereby P(A u B) would be 0.1

hence max p(AandB) would be 0.8,

I hope i made sense


It looks like you came from another angle, but it seems to me there are some mix ups. P(A) - will not snow all winter long? Anyhow, was wondering if what you meant was similar to what Sravna was saying? Thanks.



yeah i just missed that ,, you are right p(A) would be 0.9, blunder on my part ,,
_________________

Help with Kudos if I add to your knowledge realm.

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 630
Location: India
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 05 Sep 2013, 07:47
1
obs23 wrote:
Helpful guys. Appreciate your efforts. Sravna just to clarify:

We have p (A n B) = p(A) + p(B) - p(A u B)

p(A) is the probability that it will snow
p(B) is the probability that the schools will close

Quote:
p(A n B) will be maximum when p(A u B) is minimum
You mean when p(A u B) maximized, don't you?

In other words, the P(ANB) is maximized when P(AORB) is maximized and this maximization happens only when B is completely dependent on A, becoming A and P(AORB)=P(B). Seem to make sense now. Hope I won't be trapped next time.


Hi,

I meant p(A u B) is minimized i.e., the probability either A or B occurring is minimum. This minimum is equal to the higher of p(A) and p(B) because it cannot be less than that. p(A) is the higher probability. So p(AUB) is equal to p(A).

So p(A n B) = p(A) + p(B) - p(A u B) becomes
p(A n B) = p(A) + p(B) -p(A)
p(A n B) = p(B)= 0.8
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Manager
Manager
avatar
Joined: 23 May 2013
Posts: 107
GMAT ToolKit User
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 08 Sep 2013, 01:40
3
Hi Karishma

While i get the logic of your answer, i always understood that probability of event A and Probability of event B occurring is P(A)*P(B). So here is applied the same and got the answer as 0.9*0.8 = 0.72.
Whats wrong with it? Please help to explain.
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Manager
Manager
avatar
Joined: 08 Jun 2015
Posts: 105
There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 24 Jul 2015, 18:30
1
obs23 wrote:
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%

I have seen several explanations on this one and I cannot understand the point of intersection I guess...Has anyone seen similar problems they saw here (specifically with given probabilities) or perhaps I am looking for a parallel (gumballs, etc) to this problem.

There is one rule on dependent probability P(A) + P(B) - P(AB) but clearly this is not the case here. The dice are independent. With colored balls, we could calculate what happens after the balls taken away (when they are not replaced) and it makes sense. With this type of problem, I do not know what to precisely think of dependent probability :( And what is up with solving probability with overlapping sets or the matrix?

And what exactly happens when we multiply 90% and 80% conceptually? I mean what does that presume and why it is not correct? Basically, a thorough breakdown of this problem would be very helpful.

Please remember that I have seen other explanations, and my questions are based on them. Probably the best of them are:
"The greatest possible probability will occur when b is dependent on a. Thus it will be their intersection set. Hence answer = 0.8"

"They're asking for the greatest possible probability. This will occur if whenever it snows, schools close. This is a causation problem. That means schools will close only if it snows, but not all the time it snows. So you don't have to multiply .9*.8, because each time .8 occurs, .9 will be in effect as well."

I do not understand exactly what they mean...Anyway, I hope you see where I am aiming.


The greatest probability translates as "take the range of probabilities of these two events occurring under different circumstances, and choose the greatest extreme."

If event B is fully dependent on event A, then the probability is equal to the smallest probability of either event A or B, 0.8.

If event B is not fully dependent on event A, then the maximum we can know for sure is 0.72, or event A * event B.

So, the range of possibilities is 0.72 to 0.8. The greatest possibility is 0.8 or 80%.
Manager
Manager
avatar
Joined: 24 Jul 2011
Posts: 187
Location: India
GMAT 1: 570 Q50 V19
GMAT 2: 650 Q49 V28
GMAT 3: 690 Q50 V34
WE: Information Technology (Investment Banking)
GMAT ToolKit User Reviews Badge
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 04 Oct 2015, 23:38
1
Basically, the probability is 0.72 when both of the events are mutually exclusive. When they are dependent you got to use the equation

P(AUB) = P(A) + P(B) - P(A intersection B)
_________________

Middle of nowhere!

Manager
Manager
avatar
B
Joined: 14 Jul 2014
Posts: 175
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Reviews Badge
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 30 Dec 2015, 11:40
Could someone please explain how P(A intersection B) is calculated differently from P(A U B)? Thanks
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India
There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 30 Dec 2015, 21:14
3
2
dina98 wrote:
Could someone please explain how P(A intersection B) is calculated differently from P(A U B)? Thanks


A intersection B is whatever is common between the two sets.

Either you will be given its value or if they are independent events, then P(A intersection B) = P(A) * P(B).

For mutually exclusive events, P(A intersection B) = 0. Mutually exclusive events are those which cannot happen at the same time such as "Getting heads on flipping a coin" and "Getting tails on flipping a coin".

When there is some dependence in the events, the maximum value the intersection can have is the lower of the two probabilities.
Say P(A) = 0.4 and P(B) = 0.7.
The maximum probability of intersection can be 0.4 because P(A) = 0.4.
The minimum value of P(A intersection B) will be 0.1 since probability cannot exceed 1 so P(A U B) is maximum 1.
1 = 0.4 + 0.7 - P(A intersection B)
P(A intersection B) = 0.1 (at least)

Actual value of P(A intersection B) will lie somewhere between 0.1 and 0.4 (inclusive)


A union B is the sum of whatever is common between them and the elements which are contained in one set only.
P(A U B) = P(A) + P(B) - P(A intersection B)
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1114
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 30 Nov 2017, 23:46
1
Max probability of both event A & B = least value of A or B 
this is because P(A& B) = P(A)*P(B) , if the events are independent.
P(A& B) = P(A)*P(B/A) , if the events are independent.
now since the max value of probability for any event P(B) or P(B/A)= 1, hence max probability of both events = min of probability of individual events.
Here probability of snow P(A) =0.9
Probability of school closing, P(B) =0.8
Hence probability of their intersection =0.8.
Hope it is clear.
Please provide Kudos if u like the solution.

Sent from my 2014818 using GMAT Club Forum mobile app
_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior Manager
Senior Manager
avatar
S
Joined: 15 Jan 2017
Posts: 356
Re: There is a 10% chance that it won't snow all winter long  [#permalink]

Show Tags

New post 11 Dec 2017, 23:40
Woah, that was 700 level, so cool. Somehow, it reminds me of puzzles.

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%

If we break it up - "There is a 10% chance that it won't snow all winter long. 90% chance it will snow

Then - "There is a 20% chance that schools will not be closed all winter long" - 80% chance it will be closed.

Question- What is the greatest possible probability that it will snow and schools will be closed during the winter? - max possibility of 90% snow and 80% closing --> which means "greatest possibility" is 80% [max chance is 80%]

Obviously, this isn't the right mathematical approach, but this is what occurred to me, and it didn't need too many calculations.
Kudos, if it was useful for you :)
GMAT Club Bot
Re: There is a 10% chance that it won't snow all winter long &nbs [#permalink] 11 Dec 2017, 23:40
Display posts from previous: Sort by

There is a 10% chance that it won't snow all winter long

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.