GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Sep 2018, 11:04

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

At a blind taste competition a contestant is offered 3 cups

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
B
Joined: 29 Nov 2016
Posts: 53
At a blind taste competition a contestant is offered 3 cups  [#permalink]

Show Tags

New post 20 Feb 2018, 21:05
In the second approach why don't we multiply by \(C^1_2\) while selecting the second or third tea type?



Bunuel wrote:
Economist wrote:
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?

# \(\frac{1}{12}\)
# \(\frac{5}{14}\)
# \(\frac{4}{9}\)
# \(\frac{1}{2}\)
# \(\frac{2}{3}\)


And the good one again. +1 to Economist.

"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind).

\(\frac{C^2_3*C^4_6}{C^4_9}=\frac{5}{14}\).

\(C^2_3\) - # of ways to choose which 2 samples will be tasted;
\(C^4_6\) - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups);
\(C^4_9\) - total # of ways to choose 4 cups out of 9.

Answer: B.

Another way:

Calculate the probability of opposite event and subtract this value from 1.

Opposite event is that contestant will taste ALL 3 samples, so contestant should taste 2 cups of one sample and 1 cup from each of 2 other samples (2-1-1).

\(C^1_3\) - # of ways to choose the sample which will provide with 2 cups;
\(C^2_3\) - # of ways to chose these 2 cups from the chosen sample;
\(C^1_3\) - # of ways to chose 1 cup out of 3 from second sample;
\(C^1_3\) - # of ways to chose 1 cup out of 3 from third sample;
\(C^4_9\) - total # of ways to choose 4 cups out of 9.

\(P=1-\frac{C^1_3*C^2_3*C^1_3*C^1_3}{C^4_9}=1-\frac{9}{14}=\frac{5}{14}\).

Answer: B.

Hope it's clear.
Economist GMAT Tutor Discount CodesMagoosh Discount CodesEMPOWERgmat Discount Codes
Intern
Intern
avatar
B
Joined: 17 Jul 2018
Posts: 14
At a blind taste competition a contestant is offered 3 cups  [#permalink]

Show Tags

New post 12 Aug 2018, 19:09
Mudit27021988 wrote:
In the second approach why don't we multiply by \(C^1_2\) while selecting the second or third tea type?



Bunuel wrote:
Economist wrote:
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?

# \(\frac{1}{12}\)
# \(\frac{5}{14}\)
# \(\frac{4}{9}\)
# \(\frac{1}{2}\)
# \(\frac{2}{3}\)


And the good one again. +1 to Economist.



"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind).

\(\frac{C^2_3*C^4_6}{C^4_9}=\frac{5}{14}\).

\(C^2_3\) - # of ways to choose which 2 samples will be tasted;
\(C^4_6\) - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups);
\(C^4_9\) - total # of ways to choose 4 cups out of 9.

Answer: B.

Another way:

Calculate the probability of opposite event and subtract this value from 1.

Opposite event is that contestant will taste ALL 3 samples, so contestant should taste 2 cups of one sample and 1 cup from each of 2 other samples (2-1-1).

\(C^1_3\) - # of ways to choose the sample which will provide with 2 cups;
\(C^2_3\) - # of ways to chose these 2 cups from the chosen sample;
\(C^1_3\) - # of ways to chose 1 cup out of 3 from second sample;
\(C^1_3\) - # of ways to chose 1 cup out of 3 from third sample;
\(C^4_9\) - total # of ways to choose 4 cups out of 9.

\(P=1-\frac{C^1_3*C^2_3*C^1_3*C^1_3}{C^4_9}=1-\frac{9}{14}=\frac{5}{14}\).

Answer: B.

Hope it's clear.


Apologies, please ignore
Intern
Intern
User avatar
B
Joined: 11 Oct 2016
Posts: 10
Location: Canada
CAT Tests
Re: At a blind taste competition a contestant is offered 3 cups  [#permalink]

Show Tags

New post 23 Aug 2018, 08:51
ScottTargetTestPrep Please help on this one. Can you provide with an alternative solution?
Intern
Intern
avatar
B
Joined: 05 Mar 2015
Posts: 48
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
CAT Tests
Re: At a blind taste competition a contestant is offered 3 cups  [#permalink]

Show Tags

New post 26 Aug 2018, 00:43
I really dont understand the question. I dont try to solve, but just simply understand the situation. I can't
Re: At a blind taste competition a contestant is offered 3 cups &nbs [#permalink] 26 Aug 2018, 00:43

Go to page   Previous    1   2   3   [ 45 posts ] 

Display posts from previous: Sort by

At a blind taste competition a contestant is offered 3 cups

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.