probability.

[Md.Nazrul Islam]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that B stock will increase in value during the next month .what is the greatest possible value that neither of these two events will occur ?

[Shalabh's Quants]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that B stock will increase in value during the next month .what is the greatest possible value that neither of these two events will occur ?

Given is P(A) = 0.54; P(Not A) = 1-0.54 = 0.46;

Similarly, P(B) = 0.68; P(Not B) = 1-0.68 = 0.32;

Prob. of none of the events to occur = P(Not A)*P(Not B) =0.46*0.32 = 0.1472.

[Stuart@KaplanGMAT]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that B stock will increase in value during the next month .what is the greatest possible value that neither of these two events will occur ?

Hello!

This is a non-GMAT question for 2 reasons. First, there are no answer choices. Second, GMAT probability always deals with INDEPENDENT events - here, not only does the question not specify that the events are independent, but it also implies that they could be dependant. After all, if they were independent the question would never read "the greatest possible value that neither" would occur, it would just ask for the probability that neither would occur.

Normally I wouldn't address a non-GMAT question (other than to warn students off of it), but this does help us understand the difference between independent and dependant, so what the heck. However, I want to reiterate, THERE IS NO CHANCE OF THIS QUESTION (or a similar one) EVER APPEARING ON THE GMAT. This smacks of a "home made" question - I'm always wary of new posters who don't include the source of their questions.

We know that stock B has a 68% chance to increase; since it has a higher % chance than A, there's no way that stock B could be dependant on stock A.

However, stock A's performance could be 100% dependant on stock B's. Since we want to MAXIMIZE the probability that neither event will occur, we want to make stock A completely dependant on B. If that's the case, then there's a 32% chance that neither event will occur. Accordingly, 32% is the correct answer to the question.

[mgm]

This problem showed up on GMATPrep 3 .

[ppravin88]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that B stock will increase in value during the next month .what is the greatest possible value that neither of these two events will occur ?

Hello!

This is a non-GMAT question for 2 reasons. First, there are no answer choices. Second, GMAT probability always deals with INDEPENDENT events - here, not only does the question not specify that the events are independent, but it also implies that they could be dependant. After all, if they were independent the question would never read "the greatest possible value that neither" would occur, it would just ask for the probability that neither would occur.

Normally I wouldn't address a non-GMAT question (other than to warn students off of it), but this does help us understand the difference between independent and dependant, so what the heck. However, I want to reiterate, THERE IS NO CHANCE OF THIS QUESTION (or a similar one) EVER APPEARING ON THE GMAT. This smacks of a "home made" question - I'm always wary of new posters who don't include the source of their questions.

We know that stock B has a 68% chance to increase; since it has a higher % chance than A, there's no way that stock B could be dependant on stock A.

However, stock A's performance could be 100% dependant on stock B's. Since we want to MAXIMIZE the probability that neither event will occur, we want to make stock A completely dependant on B. If that's the case, then there's a 32% chance that neither event will occur. Accordingly, 32% is the correct answer to the question.

This question appeared in the latest GMAT Prep Exam Pack 1!

[GMATGuruNY]

To MAXIMIZE the probability of a BAD outcome (that neither A nor B happens), we must MINIMIZE the probability of a GOOD outcome (that either A or B happens).
The probability of a good outcome will be minimized if one of the probabilities DEPENDS on the other.
Let's rephrase the problem so that one of the probabilities is more clearly dependent on the other.
Let A = John wins the lottery.
Let B = John buys a lottery ticket.
Here, the probability of A is clearly dependent on the probability of B: John can win the lottery only if he first buys a ticket.
Question rephrased:

If the probability that John wins the lottery is 0.54, and the probability that John buys a lottery ticket is 0.68, what is the 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

If John DOESN'T buy a lottery ticket, then NEITHER event will occur.
P(John doesn't buy a lottery ticket) = 1 - 0.68 = 0.32.

The correct answer is B.

Aside: If anyone knows of a lottery with these odds, please purchase a ticket on my behalf.

[Milovan]

If we need to maximize the probability that neither occur, isn't better to say that A = John buys a lottery ticket. We would then have 1 - 0,54 = 0,46
Is this wrong?

[[email protected]]

Hi Milovan,

The wording of the question asks for the probability that NEITHER even will occur (so, we're looking for the odds that John DOESN'T BUY a tick AND he DOESN'T WIN).

Your example involves John BUYING a ticket. This doesn't match what the prompt asks for, so the result is not correct.

GMAT assassins aren't born, they're made,
Rich

[Milovan]

Hi Milovan,

The wording of the question asks for the probability that NEITHER even will occur (so, we're looking for the odds that John DOESN'T BUY a tick AND he DOESN'T WIN).

Your example involves John BUYING a ticket. This doesn't match what the prompt asks for, so the result is not correct.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Maybe you misunderstand me. I have set that A = buying a lottery. Therefore P(a)=0,54 and further P(notA) = 1 - 0,54 = 0,46

So, my assumption is that if stock A does not increase stock B will not increase (reversed compared with the GMATGuruNY's assumption). In this scenario probability that neither will occur is higher, which is the task of the question.

Could you please explain me what am I missing?

Thanks

[GMATGuruNY]

If we need to maximize the probability that neither occur, isn't better to say that A = John buys a lottery ticket. We would then have 1 - 0,54 = 0,46
Is this wrong?

If P(buys a ticket) = 0.54 and P(wins) = 0.68, then the probability of buying a ticket is LESS than the probability of winning.
This makes no sense.
Clearly, it is easier to buy a ticket than to win.
Thus, probability of buying a ticket must be GREATER than probability of winning.

[Mathsbuddy]

If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that B stock will increase in value during the next month .what is the greatest possible value that neither of these two events will occur ?

Hello!

This is a non-GMAT question for 2 reasons. First, there are no answer choices. Second, GMAT probability always deals with INDEPENDENT events - here, not only does the question not specify that the events are independent, but it also implies that they could be dependant. After all, if they were independent the question would never read "the greatest possible value that neither" would occur, it would just ask for the probability that neither would occur.

Normally I wouldn't address a non-GMAT question (other than to warn students off of it), but this does help us understand the difference between independent and dependant, so what the heck. However, I want to reiterate, THERE IS NO CHANCE OF THIS QUESTION (or a similar one) EVER APPEARING ON THE GMAT. This smacks of a "home made" question - I'm always wary of new posters who don't include the source of their questions.

We know that stock B has a 68% chance to increase; since it has a higher % chance than A, there's no way that stock B could be dependant on stock A.

However, stock A's performance could be 100% dependant on stock B's. Since we want to MAXIMIZE the probability that neither event will occur, we want to make stock A completely dependant on B. If that's the case, then there's a 32% chance that neither event will occur. Accordingly, 32% is the correct answer to the question.

I don't see why differences in probability affect dependence.
Surely the probabilities are given as absolute, so Shalabh Jain's answer could not be exceeded.
Clarity on this matter would be much appreciated.
Thanks.

[Milovan]

If we need to maximize the probability that neither occur, isn't better to say that A = John buys a lottery ticket. We would then have 1 - 0,54 = 0,46
Is this wrong?

If P(buys a ticket) = 0.54 and P(wins) = 0.68, then the probability of buying a ticket is LESS than the probability of winning.
This makes no sense.
Clearly, it is easier to buy a ticket than to win.
Thus, probability of buying a ticket must be GREATER than probability of winning.

Hi Mitch,

I totally agree on that one with you. However, in the question we had, situation relates to two stocks. In that one we can not differ probabilities like you did in your example with buying a ticket and winning a lottery.

So, my question is why we took 0.68 and not 0.54 to subtract from 1 since in that case we would get higher probability? That means of course that we need to change starting assumption that rise of the stock with probability of 0.68 directly depends from the rise of the stock with probability 0.54.

Thanks

[GMATGuruNY]

So, my question is why we took 0.68 and not 0.54 to subtract from 1 since in that case we would get higher probability? That means of course that we need to change starting assumption that rise of the stock with probability of 0.68 directly depends from the rise of the stock with probability 0.54.

Thanks

Strategy:
To MINIMIZE the probability that either A or B happens, make one of the probabilities DEPENDENT on the other.
In other words:
One event will be INDEPENDENT: it can happen ON ITS OWN.
The other event will be DEPENDENT: it can happen only if the first event happens.

Since the first event can happen on its own, it's EASIER for the first event to happen.
Thus, it must have the GREATER probability.
Since the second event depends on the first event, it's HARDER for the second event to happen.
Thus, it must have the SMALLER probability.

Applying this reasoning to the problem above:
The first event -- the INDEPENDENT probability -- must be Stock B, with a probability of 0.68.
The second event -- the DEPENDENT probability -- must be Stock A, with a probability of 0.54.

[Mathsbuddy]

If we consider all these dependency arguments, then surely (?):

Assuming B is independent, but A dependends on B,
P(B independent) = 0.68
P(A which is dependent on B) = P(B and then A) = P(B independent) * P(A independent) = 0.54

So P(A independent) = 0.54/0.68 = 0.794117647

P(not A ind) = 1 - 0.794117647 = 0.205882353
P(not B ind) = 1 - 0.68 = 0.32

P(C) = P(Not A ind AND Not B ind) = 0.205882353 * 0.32 = 0.065882353

P(D) = P(Not A dep AND Not B ind) = 0.46 * 0.32 = 0.1472

P(C OR D) = 0.065882353 + 0.1472 = 0.213082353

Therefore surely the maximum probability is 0.213082353

???

[GMATGuruNY]

If we consider all these dependency arguments, then surely (?):

Assuming B is independent, but A dependends on B,
P(B independent) = 0.68
P(A which is dependent on B) = P(B and then A) = P(B independent) * P(A independent) = 0.54

So P(A independent) = 0.54/0.68 = 0.794117647

P(not A ind) = 1 - 0.794117647 = 0.205882353
P(not B ind) = 1 - 0.68 = 0.32

P(C) = P(Not A ind AND Not B ind) = 0.205882353 * 0.32 = 0.065882353

P(D) = P(Not A dep AND Not B ind) = 0.46 * 0.32 = 0.1472

P(C OR D) = 0.065882353 + 0.1472 = 0.213082353

Therefore surely the maximum probability is 0.213082353

???

You're overcomplicating the problem.
To maximize the probability of a BAD outcome (neither A nor B), we want to make it as hard as possible to get a GOOD outcome.
For this reason, we make A depend on B, so it's harder for A to happen.
(As I noted in my post above, we can't make B depend on A, since a greater probability cannot depend on a smaller probability.)

If A depends on B, then A can't happen unless B happens.
Implication:
If B doesn't happen, then NEITHER A NOR B HAPPENS (since A can't happen without B).

Thus, to account for the maximum probability that neither A nor B happens, we need only determine the probability that B doesn't happen.
Since P(B) = 0.68, P(not B) = 1 - 0.68 = 0.32.