a woman would be picked

sanju09 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 used to be picked from Room B, what is the probability that a woman would be picked?

[spoiler]Source: gmatclub.com[/spoiler]

When a man is picked from RoomA to Room B,
Probability of a woman being picked from Room B is:
3/13 * 3/8

When a women is picked from Room A to Room B,
Probability of a women beingpicked from Room B is:
10/13 * 4/9

Either of these 2 should happen.

3/13*3/8 + 10/13*4/9

Hope this helps!!

Shouldn't the first term be 3/13*4/9? (9 being the total no. of people in the room)

First Scenario
Probability of picking a woman from Room A: 10/13
Probability of picking a woman from Room B: 10/13 * 4/9

Second Scenario
Probability of picking a man from Room A: 3/13
Probability of picking a woman from Room B: 3/13 * 3/9

Total probability of picking a woman from Room B: (10/13*4/9) + (3/13*3/9) = 1/13*40/117 = 49/117

I think... :mrgreen:

Jill -- you are correct.

I accidentally wrote 4/9 instead of 3/9. My bad !

For the second scenario, probability will be 3/13*3/9