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Intern  B
Joined: 15 Jan 2016
Posts: 17
Probability Problem from OG Practice Test  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.

Please follow posting guidelines (link in my signatures). Do make sure to search for a question before you start a new thread. Topics merged. Refer above for the solution.
Math Expert V
Joined: 02 Aug 2009
Posts: 8315
Re: If the probability that Stock A will increase in value  [#permalink]

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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..

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Re: If the probability that Stock A will increase in value  [#permalink]

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Raihanuddin wrote:

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Re: If the probability that Stock A will increase in value  [#permalink]

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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: 59721
Re: If the probability that Stock A will increase in value  [#permalink]

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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!
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If the probability that Stock A will increase in value  [#permalink]

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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!

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..
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Re: If the probability that Stock A will increase in value  [#permalink]

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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?
Manager  B
Joined: 02 Mar 2017
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GMAT 1: 700 Q51 V34 Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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
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Re: If the probability that Stock A will increase in value  [#permalink]

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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
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Re: If the probability that Stock A will increase in value  [#permalink]

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Using Venn Diagrams is also a great way to solve such a question.
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If the probability that Stock A will increase in value  [#permalink]

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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
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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.
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Re: If the probability that Stock A will increase in value  [#permalink]

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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 Re: If the probability that Stock A will increase in value   [#permalink] 20 Sep 2019, 23:13

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