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In the table below, choose the two numbers - Two-Part Analys

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In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 20 Sep 2012, 05:14
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In the table below, choose the two numbers that are consistent with the information that is given. In the first column, select the row that shows the probability that at least one of the events A and B occurs, and in the second column, select the row that shows the probability that event B occurs.

Please explain how to approach such question.
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Re: In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 21 Sep 2012, 09:57
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conty911 wrote:
In the table below, choose the two numbers that are consistent with the information that is given. In the first column, select the row that shows the probability that at least one of the events A and B occurs, and in the second column, select the row that shows the probability that event B occurs.

Please explain how to approach such question.

Conty911,

I'm happy to help, but I believe something is funky about this question. Are you sure there wasn't any other text preceding the problem? There just doesn't seem to be enough information to give a sensible answer.

I am not particularly impressed with the quality of the question either --- the complicated phrase "at least one of the events A or B occurs" is a convoluted way of saying "A or B" --- in logic (at least according to the conventions GMAT follows) the word "or" implies one or the other or both --- saying "A or B happens", means A happens, or B, or both. You don't have to specify the "at least" part at all --- it's totally redundant.

Now, it's undeniably true that

P(A or B) > P(B)

so the entry in the left column must be lower than the entry in the right. At the moment, though, in the absence of any other conditions, it's not particularly clear to me that the answer couldn't be any pair in which the entry in the the left column were lower than the entry in the right. After all, P(A) could be anything, and the overlap region, P(A and B), could be anything. The requirement of P(A or B) > P(B) seems to be the only constraint in this problem. That would produce fifteen distinct right answer combinations.

Something must be missing. What is the source? What is the exact text of the question? I feel like there is some crucial condition missing.

Please let me know if you can uncover any further parts to this question.

Mike :-)
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Re: In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 09 Oct 2012, 12:05
mikemcgarry wrote:
conty911 wrote:
In the table below, choose the two numbers that are consistent with the information that is given. In the first column, select the row that shows the probability that at least one of the events A and B occurs, and in the second column, select the row that shows the probability that event B occurs.

Please explain how to approach such question.

Conty911,

I'm happy to help, but I believe something is funky about this question. Are you sure there wasn't any other text preceding the problem? There just doesn't seem to be enough information to give a sensible answer.

I am not particularly impressed with the quality of the question either --- the complicated phrase "at least one of the events A or B occurs" is a convoluted way of saying "A or B" --- in logic (at least according to the conventions GMAT follows) the word "or" implies one or the other or both --- saying "A or B happens", means A happens, or B, or both. You don't have to specify the "at least" part at all --- it's totally redundant.

Now, it's undeniably true that

P(A or B) > P(B)

so the entry in the left column must be lower than the entry in the right. At the moment, though, in the absence of any other conditions, it's not particularly clear to me that the answer couldn't be any pair in which the entry in the the left column were lower than the entry in the right. After all, P(A) could be anything, and the overlap region, P(A and B), could be anything. The requirement of P(A or B) > P(B) seems to be the only constraint in this problem. That would produce fifteen distinct right answer combinations.

Something must be missing. What is the source? What is the exact text of the question? I feel like there is some crucial condition missing.

Please let me know if you can uncover any further parts to this question.

Mike :-)


I assume P (a+b) = 1/2 of P(b) so 0.5 and 0.25 is the answer. But not sure if my assumption is true.
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Re: In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 10 Oct 2012, 08:58
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ravipprasad wrote:
I assume P (a+b) = 1/2 of P(b) so 0.5 and 0.25 is the answer. But not sure if my assumption is true.

Dear Ravipprasad,

The trouble is --- that's one possible answer, but not the only one.

It could be true that
P(A) = 0.25 and P(B) = 0.25 and P(A or B) = 0.50
or that
P(A) = 0.25 and P(B) = 0.10 and P(A or B) = 0.35
or that
P(A) = 0.10 and P(B) = 0.25 and P(A or B) = 0.35
or that
P(A) = 0.40 and P(B) = 0.10 and P(A or B) = 0.50
etc. etc.

We have no guarantee that P(A) = P(B). Furthermore, I was assuming in these four cases that A & B are disjoint, that is to say, that they have no overlap.
If A & B are disjoint, then P(A or B) = P(A) + P(B)
If A & B are not disjoint, then P(A or B) = P(A) + P(B) - P(A and B)


For example, it could be true that:
P(A) = 0.25, P(B) = 0.50, P(A and B) = 0.15, so P(A or B) = 0.60

It actually would be an excellent GMAT math question simply to count all the possible answers one could make on this chart! Either the person who wrote the question was not good at writing questions, or the person who posted it omitted crucial information. Be careful making assumptions --- in a real, well-written GMAT problem, no assumptions will be necessary, and in fact, making assumptions will just get you in trouble.

Does all this make sense?

Mike :-)
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Re: In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 11 Jun 2013, 09:08
The question posted here is incomplete.
The question (from source) clearly mentions "The events A and B are independent, and the probability that event A occurs is 0.4." and then the rest of the question.
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Re: In the table below, choose the two numbers - Two-Part Analys [#permalink] New post 11 Jun 2013, 12:59
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GmatYes wrote:
The question posted here is incomplete.
The question (from source) clearly mentions "The events A and B are independent, and the probability that event A occurs is 0.4." and then the rest of the question.

Dear GmatYes,
Thank you!! That makes a ton of sense! I was wondering what kind of source would present such a lame half-baked question. With this new information, it's actually a sensible question at last!
Thank you very much!
Mike :-)
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Re: In the table below, choose the two numbers - Two-Part Analys   [#permalink] 11 Jun 2013, 12:59
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