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There are 10 women and 3 men in Room A. One person is picked [#permalink]

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12 Aug 2010, 04:52

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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?

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

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 4974 times ]

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Re: There are 10 women and 3 men in Room A. One person is picked [#permalink]

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15 Sep 2013, 22:17

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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.

Re: There are 10 women and 3 men in Room A. One person is picked [#permalink]

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12 Nov 2014, 01:22

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Re: There are 10 women and 3 men in Room A. One person is picked [#permalink]

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01 Jan 2015, 13:08

ARUNPLDb wrote:

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.

Why do we need to multiply with the probabilities of woman/man picked from room A. After a person is moved from A to B, we will have either 3 women or 4 women. So why not just add 3/9 + 4/9?? Why to bother about the probability of picking a person from A??

Re: There are 10 women and 3 men in Room A. One person is picked [#permalink]

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01 Jan 2015, 17:43

Expert's post

Hi saurabh99,

You have to factor in the probability that a man or a woman is transferred from Room A to Room B because THAT outcome affects the probability of the next calculation. While you are correct that there will either be 3 women or 4 women in the room, the probability of one or the other is NOT the same.

Missing that part of the calculation is the equivalent of thinking "there are 3 women and 6 men in a room, so randomly picking 1 person can only lead to 2 results: 1 man or 1 woman. Thus, the odds of picking a woman are 1 in 2." Probability questions on the GMAT are almost always "weighted" - the number of each option affects the probability/calculation, so you have to factor in the "weights."

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