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

 It is currently 14 Oct 2019, 15:58 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If the probability that Stock A will increase in value

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

Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 7954
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

If probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during next month. What is greatest possible value for the probability that neither of these two events will occur
a) 0.22
b) 0.32
c) 0.37
d) 0.46
e) 0.63

Got stumped by this one. A solution is highly appreciated.

Hi,
there are a lot of solutions talked of above..
But the crux of the entire thing is...
If a Q is asking for the greatest value possible, we can infer there can be various possible values..

GREATEST:- when will it be greatest, when there is complete overlap..
that is P of both happening = P of one of them happening(ofcourse it will be lower)
so, teh P of both not happening is 1-the larger prob= 1-.68=0.32

LOWEST:- If, say, we are to find the lowest possiblity, when there is no/least possible overlap..
so P of both happening= .68 + .54 -1 = .22..
so least prob of both not happening= 1-(.68+.54-.22)=0..

_________________
Intern  Joined: 19 Jan 2016
Posts: 43
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Raihanuddin wrote:
Please check the attachment

_________________
---------------------------------------------------------
Please kudos me if this helps. Thank you.
Manager  B
Status: Manager to Damager!
Affiliations: MBA
Joined: 22 May 2014
Posts: 56
Location: United States
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel wrote:
metallicafan wrote:
IanStewart wrote:
....So if the probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32, it may be that every time B does not increase, A also does not increase. So the maximum probability that both do not increase is 0.32. Of course, it's also possible that the probability both do not increase is substantially lower than that (it could be as low as 0, in fact).

In relation to the explanation provided by IanStewart, I understand the example about the rain and clouds because there is a causality relationship behind (clouds are necessary in a rain). But in the original question, we don't know whether A depends on B or B depends on A. In this sense, we could also say that every time A does not increase, B also does not increase (the opposite stated by Ian). Consequentely, we could say that the maximum probability that both do not increase is 0.46 (which is also a choice (D)).

How could we figure out that the correct causality relationship is the mentioned by Ian?. Please explain.

Responding to a pm.

The probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32. Now, how can the probability that both do not increase be more than individual probability of not increasing for each? So the probability that both do not increase cannot be more than 0.32. Basically the probability that both do not increase is between 0 and 0.32, inclusive (in fact the moment you realize this, you have the correct answer right away).

Anyway, as Ian mentioned above, this is not a type of question you'll see on the GMAT, so I wouldn't worry about it at all.

Hi Bunuel,
This is real GMAT EP 1 question.. I too encountered today during my practice exam.
I would appreciate if you can give an easy and understandable solution...

Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

MorningRunner wrote:
Hi Bunuel,
This is real GMAT EP 1 question.. I too encountered today during my practice exam.
I would appreciate if you can give an easy and understandable solution...

Please check solutions on previous TWO pages!
_________________
Manager  B
Status: Manager to Damager!
Affiliations: MBA
Joined: 22 May 2014
Posts: 56
Location: United States
If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel wrote:
MorningRunner wrote:
Hi Bunuel,
This is real GMAT EP 1 question.. I too encountered today during my practice exam.
I would appreciate if you can give an easy and understandable solution...

Please check solutions on previous TWO pages!

I have already read Mike's and IanStewart's great explanations and solutions..
Somehow they are not convincing me..
I love you and love your quick,easy and right approach and explanations "needed at GMAT exam". That is why I asked you..
I am Q50 guy.. Just wanna hit Q51.. So wanna be sure to hit the right way..
Intern  Joined: 26 Feb 2017
Posts: 1
Location: United States
Concentration: Entrepreneurship, Sustainability
GPA: 3.9
WE: Business Development (Telecommunications)
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Question - in general. I assumed that stocks are independent and got this question wrong. I understand why now, but my question is should we always assume events could be dependent unless it is explicitly stated that they are independent?
Director  S
Joined: 17 Dec 2012
Posts: 626
Location: India
If the probability that Stock A will increase in value  [#permalink]

Show Tags

2
Baten80 wrote:
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

1.Assume a period of 100 days. So 54 days stock A will increase and 68 days stock B will increase
2. The 54 days of increase in stock A can be contained within the days of increase in stock B.
3. So the maximum number of cases when both the events do not happen is the remaining after subtracting the days of B's increase only which is 100-68=32 days
4. So the greatest probability is 32/100=0.32
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Manager  B
Joined: 02 Mar 2017
Posts: 71
GMAT 1: 700 Q51 V34 Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

How I solved-
Lets give each term a probability-
A* is the probability that Stock A rises= 0.54
B* is the probability that Stock B rises = 0.68
A is the probability that stock A does not rise = 0.46
B is the probability that stock B does not rise = 0.32

There 4 possible things that can happen- A*B* or A*B or B*A or AB. Question is neither of them happens, that is AB= 0.1472 But this is the case when they both are completely independent, and one stock does not have any effect on other.

Consider a scenario when B rises and forces A to rise, in this situation case B*A is not possible. Hence the probability that neither of them happens will increase ( note- Now we cannot calculate the neither of them happening by simply multiplying A and B, rather answer will be 1-(rest of the cases). Or a condition that whenever Stock A rises, Stock B will fall- in this case probability that neither of them happens is 0.

Now question is what is the max probability neither of them happens? Most important thing to understand is that probability of 2 simultaneous things to happen is much more difficult that either of the 2 things happens independently. So the Max Prob that neither of them happens has to be less than either 0.46 (this is not possible) or 0.32 .

0.46 is cannot be the upper limit. Why you ask? consider that possible that neither of them happen is 0.46, this probability tells us that following are the possible scenario-
A*B* or A*B or AB ( solve this using AB = 1- A*B*- A*B) - this states that whenever Stock A does not rise, stock B also does not rise. Indirectly saying that the probability that Stock B will be not rise is dependent on stock A not rising and some other factors . Hence B should be >=0.46 ( this is contrary to the fact that B=0.32).

Example
If oil price does not rise stock A and stock B will not rise.
Also if export rate does not rise stock B will not rise.

If either of the thing happens - oil price increase but export does not/ oil price does not increase but export rate increases / oil does not increase and export does not increase - Stock B will not rise.
But only oil price dictates stock A.
Hence you can conclude probability that B does not rise is much higher than probability A does not rise.

In the given question it is otherwise. A>B hence. Ans is 0.32.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

4
2
Baten80 wrote:
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

Recall that if set U is the universal set containing two sets A and B, we have:

P(U) = P(A) + P(B) - P(A and B) + P(neither A nor B)

Since P(U) = 1, we can also say:

1 = P(A) + P(B) - P(A and B) + P(neither A nor B)

If we let the probability that stock A will increase be P(A) and the probability that stock B will increase be P(B), then we are given that P(A) = 0.54 and P(B) = 0.68. Thus, we can say:

1 = 0.54 + 0.68 - P(A and B) + P(neither A nor B)

Notice that we are being asked for the greatest value of P(neither A nor B). If that is the case, we want P(A and B) to be as large as possible since we are subtracting it. However, notice that P(A and B) can’t be larger than either P(A) or P(B). Therefore, P(A and B) can be only as large as the lesser value of P(A) and P(B). So, here P(A and B) can be as large as P(A), or 0.54. Thus:

1 = 0.54 + 0.68 - 0.54 + P(neither A nor B)

1 = 0.68 + P(neither A nor B)

0.32 = P(neither A nor B)

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  B
Joined: 13 Apr 2017
Posts: 15
Location: India
Concentration: Finance, Marketing
GRE 1: Q164 V146 WE: Analyst (Computer Software)
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel wrote:
metallicafan wrote:
IanStewart wrote:
....So if the probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32, it may be that every time B does not increase, A also does not increase. So the maximum probability that both do not increase is 0.32. Of course, it's also possible that the probability both do not increase is substantially lower than that (it could be as low as 0, in fact).

In relation to the explanation provided by IanStewart, I understand the example about the rain and clouds because there is a causality relationship behind (clouds are necessary in a rain). But in the original question, we don't know whether A depends on B or B depends on A. In this sense, we could also say that every time A does not increase, B also does not increase (the opposite stated by Ian). Consequentely, we could say that the maximum probability that both do not increase is 0.46 (which is also a choice (D)).

How could we figure out that the correct causality relationship is the mentioned by Ian?. Please explain.

Responding to a pm.

The probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32. Now, how can the probability that both do not increase be more than individual probability of not increasing for each? So the probability that both do not increase cannot be more than 0.32. Basically the probability that both do not increase is between 0 and 0.32, inclusive (in fact the moment you realize this, you have the correct answer right away).

Anyway, as Ian mentioned above, this is not a type of question you'll see on the GMAT, so I wouldn't worry about it at all.

hi bunuel, this is a gmat prep exam pack 1 ques. That is this might be a retired gmat ques. Which means ques like this can come in future also.
_________________
princeton-1: 470
princeton-2: 590
princeton-3: 460
princeton-4: 610
gmat club cat: 620
manhatten-1: 680
veritas: 650
princeton-5: 700
princeton-6: 610
manhatten-2: 740
kaplan: 750
princeton-7: 700
manhatten-3: 780
gmat prep 1: 770
princeton-8: 680
manhatten-4: 780
princeton-9: 710
gmat prep 2: 740
manhatten-5: 780
princeton-10: 710
GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1811
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

IanStewart wrote:
I'd add that I don't think I've ever seen a real GMAT probability question which tests this idea, so it probably is not important to study in much detail. Fundamentally this question is dealing with overlapping sets (Venn diagrams), but the GMAT questions I've seen don't test overlapping sets using dependent probabilities.

I should probably update this comment - when I wrote the above, a few years ago, it was true (I hadn't yet seen this problem in official materials). I've since seen two official questions, including this one, that test the concept that's tested here. I've seen a few thousand official questions by now, so two is a tiny number, and what I said should still be true; it's very unlikely you'll see this kind of question on a real test. But it's not impossible.
_________________
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
Intern  B
Joined: 09 Jun 2016
Posts: 24
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel This question is there in GMAT Prep Exam Pack 1. Looks like now they're serving such questions in GMAT. It will be great if you can put up a link for similar questions.
_________________
..................................................................................................................
micro-level speed, macro-level patience | KUDOS for the post ,shall be appreciated the most
Manager  S
Joined: 10 Sep 2015
Posts: 66
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31 GMAT 2: 660 Q47 V35 GMAT 3: 700 Q49 V36 GPA: 4
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel wrote:
metallicafan wrote:
IanStewart wrote:
....So if the probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32, it may be that every time B does not increase, A also does not increase. So the maximum probability that both do not increase is 0.32. Of course, it's also possible that the probability both do not increase is substantially lower than that (it could be as low as 0, in fact).

In relation to the explanation provided by IanStewart, I understand the example about the rain and clouds because there is a causality relationship behind (clouds are necessary in a rain). But in the original question, we don't know whether A depends on B or B depends on A. In this sense, we could also say that every time A does not increase, B also does not increase (the opposite stated by Ian). Consequentely, we could say that the maximum probability that both do not increase is 0.46 (which is also a choice (D)).

How could we figure out that the correct causality relationship is the mentioned by Ian?. Please explain.

Responding to a pm.

The probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32. Now, how can the probability that both do not increase be more than individual probability of not increasing for each? So the probability that both do not increase cannot be more than 0.32. Basically the probability that both do not increase is between 0 and 0.32, inclusive (in fact the moment you realize this, you have the correct answer right away).

Anyway, as Ian mentioned above, this is not a type of question you'll see on the GMAT, so I wouldn't worry about it at all.

Hi Bunuel,
I got this question in GMATprep Exam pack one, second exam.
Could you please share more question of the same kind and suggest some techniques to improve probability. Probability is something i am not able to handle. I have my exam on 20th of this month, please tell some tips for probability.

Thanks
Attachments 2017-09-08.png [ 1.29 MiB | Viewed 1500 times ] S
Joined: 06 Mar 2017
Posts: 189
Concentration: Operations, General Management
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Bunuel wrote:
metallicafan wrote:
IanStewart wrote:
....So if the probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32, it may be that every time B does not increase, A also does not increase. So the maximum probability that both do not increase is 0.32. Of course, it's also possible that the probability both do not increase is substantially lower than that (it could be as low as 0, in fact).

In relation to the explanation provided by IanStewart, I understand the example about the rain and clouds because there is a causality relationship behind (clouds are necessary in a rain). But in the original question, we don't know whether A depends on B or B depends on A. In this sense, we could also say that every time A does not increase, B also does not increase (the opposite stated by Ian). Consequentely, we could say that the maximum probability that both do not increase is 0.46 (which is also a choice (D)).

How could we figure out that the correct causality relationship is the mentioned by Ian?. Please explain.

Responding to a pm.

The probability that stock A does not increase is 0.46, and the probability that stock B does not increase is 0.32. Now, how can the probability that both do not increase be more than individual probability of not increasing for each? So the probability that both do not increase cannot be more than 0.32. Basically the probability that both do not increase is between 0 and 0.32, inclusive (in fact the moment you realize this, you have the correct answer right away).

Anyway, as Ian mentioned above, this is not a type of question you'll see on the GMAT, so I wouldn't worry about it at all.

Bunuel,
This is a question from GMATPrep EP 1, how can we suppose that this question is not GMAT type?
Though your solution has made it too easy to understand, kudos to your solution Intern  B
Joined: 09 Apr 2018
Posts: 20
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Using Venn Diagrams is also a great way to solve such a question.
Attachments

File comment: Stock A Stock B Venn Probability - Stock A Stock B.jpg [ 39.89 KiB | Viewed 764 times ]

Senior Manager  P
Joined: 10 Apr 2018
Posts: 266
Location: United States (NC)
If the probability that Stock A will increase in value  [#permalink]

Show Tags

chetan2u wrote:
If probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during next month. What is greatest possible value for the probability that neither of these two events will occur
a) 0.22
b) 0.32
c) 0.37
d) 0.46
e) 0.63

Got stumped by this one. A solution is highly appreciated.

Hi,
there are a lot of solutions talked of above..
But the crux of the entire thing is...
If a Q is asking for the greatest value possible, we can infer there can be various possible values..

GREATEST:- when will it be greatest, when there is complete overlap..
that is P of both happening = P of one of them happening(ofcourse it will be lower)
so, teh P of both not happening is 1-the larger prob= 1-.68=0.32

LOWEST:- If, say, we are to find the lowest possiblity, when there is no/least possible overlap..
so P of both happening= .68 + .54 -1 = .22..
so least prob of both not happening= 1-(.68+.54-.22)=0..

Hichetan2u,
Need help in understinding how you calculated the higlighted portion.

TO caluclte both happeinign we need to have info about both not happening ( or neither which we refer to set terminology)
Say T = A +B +X+N
Where A = only A, B = only B ,X= Both A&B , N = Neither A Nor B
T= A+B+X+N
or
T= ( A+X) +(B+X) - Both (A&B)+ N ------ (II)

So for caluclting the values of both don't we need to know the values of neither A &B
Here is what i mean
only A= $$A\overline{\rm B}$$
only B= $$\overline{\rm A}B$$
both A and B = AB
Neither A&B= $$\overline{\rm AB}$$
total

1= $$A\overline{\rm B}$$+$$\overline{\rm A}B$$+AB+$$\overline{\rm AB}$$

using formula II
100%= 68%+52% - Both +N
Both = 68%+52%-100% +N

Als0 for calculating neither don't we need the value of Both A & B
here is what i mean
100%= 68%+52%-both+N
Then N= 100%- (68%+52%-both)

What did i miss?

Probus
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Math Expert V
Joined: 02 Aug 2009
Posts: 7954
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Probus wrote:
chetan2u wrote:
If probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during next month. What is greatest possible value for the probability that neither of these two events will occur
a) 0.22
b) 0.32
c) 0.37
d) 0.46
e) 0.63

Got stumped by this one. A solution is highly appreciated.

Hi,
there are a lot of solutions talked of above..
But the crux of the entire thing is...
If a Q is asking for the greatest value possible, we can infer there can be various possible values..

GREATEST:- when will it be greatest, when there is complete overlap..
that is P of both happening = P of one of them happening(ofcourse it will be lower)
so, teh P of both not happening is 1-the larger prob= 1-.68=0.32

LOWEST:- If, say, we are to find the lowest possiblity, when there is no/least possible overlap..
so P of both happening= .68 + .54 -1 = .22..
so least prob of both not happening= 1-(.68+.54-.22)=0..

Hichetan2u,
Need help in understinding how you calculated the higlighted portion.

TO caluclte both happeinign we need to have info about both not happening ( or neither which we refer to set terminology)
Say T = A +B +X+N
Where A = only A, B = only B ,X= Both A&B , N = Neither A Nor B
T= A+B+X+N
or
T= ( A+X) +(B+X) - Both (A&B)+ N ------ (II)

So for caluclting the values of both don't we need to know the values of neither A &B
Here is what i mean
only A= $$A\overline{\rm B}$$
only B= $$\overline{\rm A}B$$
both A and B = AB
Neither A&B= $$\overline{\rm AB}$$
total

1= $$A\overline{\rm B}$$+$$\overline{\rm A}B$$+AB+$$\overline{\rm AB}$$

using formula II
100%= 68%+52% - Both +N
Both = 68%+52%-100% +N

Als0 for calculating neither don't we need the value of Both A & B
here is what i mean
100%= 68%+52%-both+N
Then N= 100%- (68%+52%-both)

What did i miss?

Probus

N= 100%- (68%+52%-both) = 100+both-68-52=both-20
Now we are looking for the least value of N,
This will happen when the positive value on other side that is BOTH is least..

so lets check for least possible value, both can be least 68+52-100=20
so N is 20-20=0

Remember we are NOT looking for exact value of N, we are looking for the greatest and least value with the info given..
and so you can play around with value of BOTH to get the greatest and lowest value of N.
_________________
Intern  B
Joined: 14 May 2018
Posts: 17
Location: United States
Concentration: Strategy, Finance
GMAT 1: 700 Q47 V40 GPA: 3.39
WE: Consulting (Accounting)
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Out of 100 days stock B goes down 32 times.
Out of the same 100 days Stock A goes down 46 times.
What is the total number of days that both stock B and stock A go down?

32.
SVP  P
Joined: 03 Jun 2019
Posts: 1684
Location: India
Re: If the probability that Stock A will increase in value  [#permalink]

Show Tags

Baten80 wrote:
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

Asked: If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

P(A) = .54
1- P(A) = .46
P(B) = .68
1- P(B) = .32

Maximum overlap between 1 - P(A) & 1 - P(B) = .32

IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Re: If the probability that Stock A will increase in value   [#permalink] 20 Sep 2019, 23:13

Go to page   Previous    1   2   [ 39 posts ]

Display posts from previous: Sort by

If the probability that Stock A will increase in value

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

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