People Mover

[thapliyalabhi]

This is a Manhattan GMAT question bank word problem.

There are 10 women and 3 men in room A. One person is picked at random from room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?

(A)13/21
(B)49/117
(C)40/117
(D)15/52
(E)5/18

The solution has been given as 10/13* 4/9+3/13 * 3/9

My doubt is when the question asks about the probability that a woman will be picked, does that mean the probability that a woman is picked from room B. If that is the case, can't we just solve the question like this:

Room B has either 4W & 5M OR 3W & 6M.
So, probability of selecting a woman from B = 4/9 + 3/9=>7/9

Please tell what is wrong here.

[RonPurewal]

This is a Manhattan GMAT question bank word problem.

There are 10 women and 3 men in room A. One person is picked at random from room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?

(A)13/21
(B)49/117
(C)40/117
(D)15/52
(E)5/18

The solution has been given as 10/13* 4/9+3/13 * 3/9

My doubt is when the question asks about the probability that a woman will be picked, does that mean the probability that a woman is picked from room B. If that is the case, can't we just solve the question like this:

Room B has either 4W & 5M OR 3W & 6M.
So, probability of selecting a woman from B = 4/9 + 3/9=>7/9

Please tell what is wrong here.

well, you should actually be able to tell that this solution (7/9) is wrong by pure common sense, without having to calculate anything.
just think about it -- in both possibilities, less than half the people in room B are female. so, clearly, your probability must work out to be less than 1/2; it's more likely that you'll pick a man, no matter what happens.

the problem is that you're missing the 10/13 and the 3/13 that need to be multiplied by these fractions. this choice is the second event in a series of two events, so you must account for the first event, too.

if you still don't see what's wrong here, change the initial setup of room B to 6 women and 2 men, and then work the problem again; your method will give a probability of greater than 1, which doesn't make any sense.

[thapliyalabhi]

This is a Manhattan GMAT question bank word problem.

There are 10 women and 3 men in room A. One person is picked at random from room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?

(A)13/21
(B)49/117
(C)40/117
(D)15/52
(E)5/18

The solution has been given as 10/13* 4/9+3/13 * 3/9

My doubt is when the question asks about the probability that a woman will be picked, does that mean the probability that a woman is picked from room B. If that is the case, can't we just solve the question like this:

Room B has either 4W & 5M OR 3W & 6M.
So, probability of selecting a woman from B = 4/9 + 3/9=>7/9

Please tell what is wrong here.

well, you should actually be able to tell that this solution (7/9) is wrong by pure common sense, without having to calculate anything.
just think about it -- in both possibilities, less than half the people in room B are female. so, clearly, your probability must work out to be less than 1/2; it's more likely that you'll pick a man, no matter what happens.

the problem is that you're missing the 10/13 and the 3/13 that need to be multiplied by these fractions. this choice is the second event in a series of two events, so you must account for the first event, too.

if you still don't see what's wrong here, change the initial setup of room B to 6 women and 2 men, and then work the problem again; your method will give a probability of greater than 1, which doesn't make any sense.

Super Ron !
Thanks. So, just because I didn't consider the first event, my probability is coming more than expected.

[RonPurewal]

Yes.

What's even more important is that you recognize at once that 7/9 is definitely the wrong answer.
if any answer ever violates common sense, don't pick it, even if you find it in the answer choices.