Last visit was: 15 Jul 2024, 14:22 It is currently 15 Jul 2024, 14:22
Toolkit
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

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.

A jar contains 12 marbles consisting of an equal number of red, green,

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 04 Apr 2010
Posts: 66
Own Kudos [?]: 202 [19]
Given Kudos: 17
Concentration: MBA, Finance, 2009
Schools:UCLA Anderson
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30806 [6]
Given Kudos: 799
General Discussion
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3649 [3]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Manager
Joined: 04 Apr 2010
Posts: 66
Own Kudos [?]: 202 [1]
Given Kudos: 17
Concentration: MBA, Finance, 2009
Schools:UCLA Anderson
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
1
Kudos
Thanks Engr2012. You are correct. I edited the question to reflect your comment.

There's a simpler way to solve the problem without using combinations.
Veritas Prep GMAT Instructor
Joined: 15 Jul 2015
Posts: 109
Own Kudos [?]: 182 [3]
Given Kudos: 11
GPA: 3.62
WE:Corporate Finance (Consulting)
A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
2
Kudos
1
Bookmarks
Think of it this way: there are initially 12 marbles that can be selected, 4 of each color. So, the odds of selecting any one color on the first pull is 1/3. Say that you select a Red marble, the odds of selecting a Red marble on the second pull is 3/11 (3 red marbles left out of the 11 marbles). The third pull then leaves you with the probability of 2/10 or 1/5 in selecting a Red marble. Finally, on the last pull, you have a 1/9 probability of selecting the last Red marble. Now, the question is reall yasking what the probability of selecting the same color marble on each of the first 4 selections is. That would be expressed as 1/3 x 3/11 x 1/5 x 1/9. Factoring the 3's out of the numerator and denominator leaves us with 1/11 x 1/5 x/ 1/9, or 1/495. Answer A is correct.

However, since there are 3 separate colors and thus, 3 ways to achieve the result, the correct answer is 3 x 1/495, or 1/165. I stand corrected.

*** REVISION - A better way to think of this is that, really, the first selection does not even matter. You WILL select a marble - thus, the Probability is 1/1. What mattters is that the following three selections all return the same color as the 1st. As a result, we have 1/1 x 3/11 x 2/10 x 1/9, or 3/11 x 1/5 x 1/9 = 3/495 0r 1/165.

Originally posted by VeritasPrepDennis on 16 Jul 2015, 12:18.
Last edited by VeritasPrepDennis on 17 Jul 2015, 09:08, edited 4 times in total.
Manager
Joined: 04 Apr 2010
Posts: 66
Own Kudos [?]: 202 [1]
Given Kudos: 17
Concentration: MBA, Finance, 2009
Schools:UCLA Anderson
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
1
Kudos
I agree that the chance of selecting one color four times in a row is 1/495. However, couldn't this happen in 3 different ways, since there are three colors? That would make the answer 3 * 1/495 = 3/495 = 1/165.

In other words, you can select any color marble on the first attempt. Then, you have to select the same color marble on the next three attempts. This would make the calculation

1/1 * 3/11 * 2/10 * 1/9 = 1/165
Manager
Joined: 28 Jun 2015
Posts: 247
Own Kudos [?]: 295 [1]
Given Kudos: 47
Concentration: Finance
GPA: 3.5
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
1
Kudos
Jar contains {4-red, 4-green, 4-blue} marbles. We are asked to find the probability that after removing 4 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.

Sample space = 12C4 = 495.

Probability of choosing 4 red = 4C4/12C4 = 1/495.
Probability of choosing 4 green = 4C4/12C4 = 1/495.
Probability of choosing 4 blue = 4C4/12C4 = 1/495.

Required probability = 1+1+1/495 = 3/495 = 1/165. Ans (B).
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3649 [0]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
TheGmatTutor wrote:
Thanks Engr2012. You are correct. I edited the question to reflect your comment.

There's a simpler way to solve the problem without using combinations.

Sure. But I feel it is always straightforward if I stick to first principles for Probability, Permutations and combinations. This way , scope of error reduces atleast for me.

Good question though based on the % of correct responses.
Intern
Joined: 15 Jan 2017
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 65
Schools: HBS '20
GMAT 1: 560 Q42 V25
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]

Statement 1: Find formula for 5/12 probability

b=black marbles, w=white marbles, T=total marbles

b/T * b-1/T-1 = 5 /12 Trial error: 2/3*1/2 /= 5/12 .... 6/9*5/8= 30/72 = 5/12 --> sufficient

w/T=1/3 and w-1/T-1 = 1/4 --> solve for w --> sufficient

Time: 2:30 min
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6570 [1]
Given Kudos: 1646
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
1
Kudos
TheGmatTutor wrote:
A jar contains 12 marbles consisting of an equal number of red, green, and blue marbles. Four marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the four marbles have been removed?

(A) 1/495
(B) 1/165
(C) 1/81
(D) 1/3
(E) 1/2

There are 4 red, 4 green, and 4 blue marbles in the jar.

If two colors are to remain in the jar after 4 are removed, all 4 marbles removed must be of the same color, that is, they are all red, or all green, or all blue.

Since there are equal number of each color, we can determine the probability of getting all marbles of one color removed and then multiply by 3 (because there are 3 colors of marbles).

The number of ways to get all red marbles is:

4C4 = 1

The total number of ways to select 4 marbles from 12 is:

12C4 = 12!/[4!(12-4)!] = 12!/(4!8!) = (12 x 11 x 10 x 9)/(4 x 3 x 2) = (11 x 5 x 9) = 495

Thus, the probability that all red marbles are removed is 4C4/12C4 = 1/495. However, since there are 3 ways to get all marbles of the same color, the the probability that all same-colored marbles are removed is is 1/495 x 3 = 3/495 = 1/165.

Intern
Joined: 02 Feb 2020
Posts: 26
Own Kudos [?]: 3 [0]
Given Kudos: 702
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
TheGmatTutor wrote:
A jar contains 12 marbles consisting of an equal number of red, green, and blue marbles. Four marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the four marbles have been removed?

(A) 1/495
(B) 1/165
(C) 1/81
(D) 1/3
(E) 1/2

Source: Original question

Total outcomes of selecting a pack of 4 balls out of 12 = 12C4=495

If a pack of four balls of any single colour is selected,then only two colors remain. Therefore total desired outcomes of getting packs of 4 balls of same colour=3( packs of 4 balls of same colour)

Therefore required probability = 3/495= 1/165

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 33980
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
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: A jar contains 12 marbles consisting of an equal number of red, green, [#permalink]
Moderator:
Math Expert
94354 posts