Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

12 Aug 2010, 03:52

2

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

67% (02:23) correct
33% (01:08) wrong based on 226 sessions

HideShow timer Statistics

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 6614 times ]

_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

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

Show Tags

15 Sep 2013, 21:17

1

This post received KUDOS

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]

Show Tags

12 Nov 2014, 00:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

Show Tags

01 Jan 2015, 12:08

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??

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."

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

Show Tags

16 Jul 2016, 12:22

1

This post received KUDOS

saurabh99 wrote:

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??

Thanks, Saurabh

Hi Saurabh,

Picking a member from room B is a dependant event. What is it dependant on ?

As the question reads out " one person is picked from room A AND moved to room B. If a single person is THEN to be picked from B"--> Here FIRST a person is moved THEN picked. So whenever you see such a dependancy , you need to first figure the number of ways of doing the first action.

Whats the first event/action ? Picking and moving a person from room A.

What are our options for event 1 ? Either a man or a woman will be picked.

Hence P(W)= 10/13 or P(M) = 3/13

Now why do we multiply ?

Lets say from point A to B there are 2 ways & from point B to C there are 2 more ways ( No direct route from A to C). How many ways do you have from A to C ?

Total number of ways from A to C= ( # of way from A to B ) * (# of ways from B to C) = 2*2 =4

Coming back to the original question:

Case 1: A woman was picked from room A and a woman was picked from room B

P(W from room A|| W from room B)= (10/13) * (4/9) Case 2: A man was picked from room A and a woman was picked from room B

P(M from room A|| W from room B)= (3/13) * (3/9)

Total probability: case 1 + case 2 ( This is an or case wherein you add the probabilities)

= (40/117) + (1/13) = 49/117

Regards, Shradha

gmatclubot

There are 10 women and 3 men in Room A. One person is picked
[#permalink]
16 Jul 2016, 12:22

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...