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Good old probability

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Master | Next Rank: 500 Posts
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by alex.gellatly » Sat Jun 23, 2012 8:10 pm
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
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by gmat_and_me » Sat Jun 23, 2012 8:54 pm
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
Top
Join the discussion
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QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Sat Mar 05, 2011 9:14 amFollowed by: 5 members
Location: Bangalore
Thanked: 20 times
GMAT Score:770

by gmat_and_me » Sat Jun 23, 2012 9:04 pm
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
Top
Join the discussion
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QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 435
Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members
Thanked: 48 times

by alex.gellatly » Sat Jun 23, 2012 9:45 pm
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.
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