Problem Solving

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?

13/21
49/117
40/117
15/52
5/18

The resultant probability has to be the product of probabilities
of selecting one woman from room A and afterwards selecting a
woman from room B.

Probability of selecting one woman from room A = 10/13
Resultant probability = (10/13) * (4/9) = 40/117

HTH

alex.gellatly wrote: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?

13/21
49/117
40/117
15/52
5/18

I think, I wrote it too fast. My bad. There is one more
possibility. You can select one man from room A and then
select a woman from room B. In that case P will be

(3/13) * (3/9) = 9/117

Since, either of these two can happen, the resultant probability
will then be the sum of the two => 40/117 + 9/117 = 49/117.

HTH

gmat_and_me wrote:The resultant probability has to be the product of probabilities
of selecting one woman from room A and afterwards selecting a
woman from room B.

Probability of selecting one woman from room A = 10/13
Resultant probability = (10/13) * (4/9) = 40/117

HTH

alex.gellatly wrote: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?

13/21
49/117
40/117
15/52
5/18

gmat_and_me wrote:I think, I wrote it too fast. My bad. There is one more
possibility. You can select one man from room A and then
select a woman from room B. In that case P will be

(3/13) * (3/9) = 9/117

Since, either of these two can happen, the resultant probability
will then be the sum of the two => 40/117 + 9/117 = 49/117.

HTH

gmat_and_me wrote:The resultant probability has to be the product of probabilities
of selecting one woman from room A and afterwards selecting a
woman from room B.

Probability of selecting one woman from room A = 10/13
Resultant probability = (10/13) * (4/9) = 40/117

HTH

alex.gellatly wrote: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?

13/21
49/117
40/117
15/52
5/18

Yes, the OA is B. I made your same mistake at first as well.