Given is P(A) = 0.54; P(Not A) = 1-0.54 = 0.46;Md.Nazrul Islam wrote: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!Md.Nazrul Islam wrote: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 ?
Stuart Kovinsky wrote:Hello!Md.Nazrul Islam wrote: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 ?
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.
If John DOESN'T buy a lottery ticket, then NEITHER event will occur.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
Hi Rich,[email protected] wrote: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
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.Milovan wrote: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?
I don't see why differences in probability affect dependence.Stuart Kovinsky wrote:Hello!Md.Nazrul Islam wrote: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 ?
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.
Hi Mitch,GMATGuruNY wrote: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.Milovan wrote: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?
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.
Strategy:Milovan wrote: 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
You're overcomplicating the problem.Mathsbuddy wrote: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
???
