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There are 10 women and 3 men in Room A. One person is picked [#permalink]
12 Aug 2010, 03:52

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This post received KUDOS

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Difficulty:

35% (medium)

Question Stats:

68% (02:03) correct
32% (00:50) wrong based on 28 sessions

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?

Re: Probability Question [#permalink]
14 Aug 2010, 01:02

What is the OA? If M picked from room A, room B probability of picking W is 4/9 If W picked from room A, room B probability of picking W is 3/9

Conditional Probability P(W in B and M picked in A) = P(W given M picked in A)*P(M picked in A) = 10/13*4/9 P(W in B and W picked in A) = P(W given W picked in A)*P(W picked in A) = 3/13*3/9

Re: Probability Question [#permalink]
05 Feb 2013, 16:29

1

This post received KUDOS

HarishV 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.

{Please try solving the problem using the Conditional Probability formula}....Would be very helpful to know how to determine the probability of 2 events when occurring simultaneously}

Using a tree diagram ( see the attachement)

Hence,

WW = \frac{10}{13}*\frac{4}{9}=\frac{40}{117}

MW = \frac{3}{13}*\frac{3}{9}=\frac{9}{117}

Finally, the probability that a woman would be picked is P= \frac{40}{117} + \frac{9}{117}=\frac{49}{117}

Attachments

Prob.png [ 9.74 KiB | Viewed 1483 times ]

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Re: There are 10 women and 3 men in Room A. One person is picked [#permalink]
15 Sep 2013, 21:17

The probability that a woman is picked from room A is 10/13 the probability that a woman is picked from room B is 4/9. Because we are calculating the probability of picking a woman from room A AND then from room B, we need to multiply these two probabilities: 10/13 x 4/9 = 40/117 The probability that a man is picked from room A is 3/13. If that man is then added to room B, this means that there are 3 women and 6 men in room B. So, the probability that a woman is picked from room B is 3/9. Again, we multiply thse two probabilities: 3/13 x 3/9 = 9/117 To find the total probability that a woman will be picked from room B, we need to take both scenarios into account. In other words, we need to consider the probability of picking a woman and a woman OR a man and a woman. In probabilities, OR means addition. If we add the two probabilities, we get: 40/117 + 9/117 = 49/117 The correct answer is B.

gmatclubot

Re: There are 10 women and 3 men in Room A. One person is picked
[#permalink]
15 Sep 2013, 21:17