In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out
of the bag, what is the probability that he will have one white and one blue marble? (Assume that Bob does not replace the marbles in the bag.)
Scroll down for answer
Ans 2/9
Need help with this Manhattan Number properties guide Q
This topic has expert replies
- amandeep.hora
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Sun Jul 12, 2009 10:11 am
- Thanked: 1 times
-
- Junior | Next Rank: 30 Posts
- Posts: 29
- Joined: Fri Feb 15, 2013 8:21 am
- Thanked: 2 times
- GMAT Score:730
Hello,
There are two ways Bob can have one blue and one white marble:
1st pick - Blue --- 2nd pick - White
1st pick - White --- 2nd pick - Blue
5/10 * 2/9 = 10/90
2/10 * 5/9 = 10/90
10/90 + 10/90 = 20/90 = 2/9
There are two ways Bob can have one blue and one white marble:
1st pick - Blue --- 2nd pick - White
1st pick - White --- 2nd pick - Blue
5/10 * 2/9 = 10/90
2/10 * 5/9 = 10/90
10/90 + 10/90 = 20/90 = 2/9
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Number of ways to select 2 marbles out of 10 marbles = 10C2 = 45amandeep.hora wrote:In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble? (Assume that Bob does not replace the marbles in the bag.)
Number of ways to select one white and one blue marble = (Number of ways to select 1 white marble out of 2)*(Number of ways to select 1 blue marble out of 5) = 2*5 = 10
Hence, required probability = 10/45 = 2/9
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Whenever I'm trying to find a certain probability, it helps to stop and ask, " What exactly must occur in order for this event to happen?"amandeep.hora wrote:In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out
of the bag, what is the probability that he will have one white and one blue marble? (Assume that Bob does not replace the marbles in the bag.)
In this case, Bob can select a white marble 1st and a blue marble 2nd, or Bob can select a blue marble 1st and a white marble 2nd.
Once we have our "ors" and "ands" in order, we can create a word equation:
P(1 white and 1 blue) = P(white 1st and blue 2nd OR blue 1st and white 2nd)
= P(white 1st and blue 2nd) + P(blue 1st and white 2nd)
= [P(white 1st) x P(blue 2nd)] + [P(blue 1st) x P(white 2nd)]
= [2/10 x 5/9] + [5/10 x 2/9]
= 10/90 + 10/90
= 20/90
= [spoiler]2/9[/spoiler]
Cheers,
Brent
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
You can use the complement here, but remember that it's:ananthbi wrote:Might be a little dumb question but why can't "1- Probability" work here? Can I not do "1 - Probability[Bob chooses red marbles]"?
P(Event A occurs) = 1 - P(Event A does not occur)
In this question, if event A is selecting 1 red and 1 blue, then for the event not to occur, we need either two red or two blue.
In other words, P(1 white and 1 blue) = 1 - P(NOT 1 white and 1 blue)
= 1 - P(2 red OR 2 blue)
I'll let you continue from here (it's dinner time!)
Cheers,
Brent
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Yes, you can do that.ananthbi wrote:Might be a little dumb question but why can't "1- Probability" work here? Can I not do "1 - Probability[Bob chooses red marbles]"?
But that trick is helpful only when the number of times "the event doesn't happen" is smaller than the number of times "the event happens".
In this case, that trick will complicate your calculation as not choosing one white and one blue doesn't mean choosing 2 red only.
P(Not 1 white and 1 blue) = P(2 red) + P (2 white) + P(2 blue) + P(1st white and 2nd red) + P(1st red and 2nd white) + P(1st blue and 2nd Red) + P(1st red and 2nd blue) ---> seven possibilities
While, P(1 white and 1 blue) = P(1st blue and 2nd white) + P(1st white and 2nd blue) ---> only two possibilities
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/