BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

probability tea

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Tue Nov 08, 2011 4:42 am

probability tea

by jzebra10 » Tue Nov 29, 2011 12:09 am
I don't understand the explanation given in the book. Can someone try to explain this better?

At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?

a) 1/12
b) 5/14
c) 4/9
d) 1/2
e) 2/3

thanks!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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

by Anurag@Gurome » Tue Nov 29, 2011 12:49 am
jzebra10 wrote:I don't understand the explanation given in the book. Can someone try to explain this better?

At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?

a) 1/12
b) 5/14
c) 4/9
d) 1/2
e) 2/3

thanks!
Probability that a contestant does not taste all of the samples = 1 - probability that a contestant tastes all 3 samples.

This means that first we should find the probability that a contestant should taste 2 cups of one sample and 1 cup from each of 2 other samples.

Total no. of ways to choose 4 cups out of 9 = 9C4
No. of ways to choose the sample which provides with 2 cups = 3C1
No. of ways to choose these 2 cups from the sample chosen = 3C2
No. of ways to choose 1 cup out of 3 from the 2nd sample = 3C1
No. of ways to choose 1 cup out of 3 from the 3rd sample = 3C1

So, probability that a contestant tastes all 3 samples = (3C1 * 3C2 * 3C1 * 3C1)/9C4 = (3 * 3 * 3 * 3)/(18 * 7) = 9/14

Therefore, required probability = 1 - 9/14 = [spoiler]5/14[/spoiler]

The correct answer is B.
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/
Top
User avatar
Legendary Member
Posts: 588
Joined: Sun Oct 16, 2011 9:42 am
Location: New Delhi, India
Thanked: 130 times
Followed by:9 members
GMAT Score:720

by rijul007 » Tue Nov 29, 2011 12:55 am
Total no of ways of tasting 4 cups of tea = 9P4 = 6*7*8*9

No of ways that all three samples are selected =>
Selecting two of a kind = 3*3C2 = 9
Other two cups different types = 3*3 = 9
Arranging them = 4!

Total no of ways = 9*9*4!

Probability that a contestant tastes all samples = P1 = 9*9*4!/6*7*8*9 = 9/14

probability that a contestant does not taste all of the samples = 1-P1 = 1- 9/14 = 5/14

IMO: B
Top
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

by shankar.ashwin » Tue Nov 29, 2011 12:58 am
You could also do it directly,

Since there are only 3 cups of each type, we can be sure he tastes 2 varieties of tea (Since he tastes a total of 4).

We have 3 samples and we taste only 2 - 3C2 = 3 ways of choosing which 2 to taste

And once we select the 2 samples, we have 6 cups of the 2 samples and we pick 4 - 6C4 = 15

Total ways = 9C4 = 126

So, we have (3*15)/126 = 5/14 (3C2*6C4/9C4)
Top
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Tue Nov 29, 2011 12:58 am
Base: 4 out of 9 has to be chosen = 9C4

Does not taste all flavours = 1- tastes all flavours

Conditions to taste all flavours = 3*( 3c1*3c1*3c2) = 3^4

result = 1- 3^4/ 9c4 = 1- 9/14 = 5/14
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.
Top
Post new topic Post Reply
• Page 1 of 1