Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Mar 2016
Posts: 131
Location: France
GPA: 3.25

A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar [#permalink]
Show Tags
03 May 2016, 13:43
Question Stats:
67% (01:49) correct 33% (02:51) wrong based on 66 sessions
HideShow timer Statistics
Hello everyone, I try to solve a probability question trough 2 different approaches : proba, AND combinatorics ... I don't understand how to do it with combinatorics . Can you help me please ? Or do you have another and more efficient way ? This is the problem :A Jar of marble contains 6 yellow and 4 blue marbles, and no other marbles. If four are pulled out of the jar, one after the other, without being replaced, what is the probability that exactly two of the four marbles will be yellow and two blue.
A 1/10 B 1/7 C 1/6 D 3/7 9 9/11 My answer number :
There is 6 possibilities to arrange 2 yellow and 2 blue (let's write YYBB) according to the MISSISSIPPI rule : \(\frac{4 !}{2 x 2}\) = 6
Here are the 6 different possibilities : YYBB, YBYB, YBBY, BYBY, BYYB, BBYY
So now, let's calculate the probabilities :
P (YYBB or YBYB or YBBY or BYBY or BYYB or BBYY ) = P (YYBB) + P(YBYB) + P(YBBY + P(BYBY) + P(BYYB) + P(BBYY ), since the outcomes are all mutually exclusives.
P(YYBB) =\(\frac{6 * 5 * 4 * 3}{10 * 9 * 8 * 7}\) = \(\frac{1}{14}\)
Each expression is equal so : P (YYBB or YBYB or YBBY or BYBY or BYYB or BBYY ) = 6* \(\frac{1}{14}\) =\(\frac{3}{7}\)
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 12 Jun 2015
Posts: 79

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar [#permalink]
Show Tags
03 May 2016, 13:59
2
This post was BOOKMARKED
4 marbles out of the given 10 are pulled out of the jar, one after the other, without being replaced
The number of possible combinations (total events) = 10C4
We need to find the probability that exactly two of the four marbles will be yellow(out of 6) and two blue( out of 4).
Here the order in which the marbles are removed isn't asked. So no permutation reqd.
The number of possible combinations to such a specific event = 6C2 X 4C2
The Probability of the specific event = [ 6C2 X 4C2 ] / 10C4
= 15 X 6 / 210 = 3/7 Correct Option : D



Math Expert
Joined: 02 Sep 2009
Posts: 44566

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar [#permalink]
Show Tags
03 May 2016, 14:01
Alex75PAris wrote: Hello everyone, I try to solve a probability question trough 2 different approaches : proba, AND combinatorics ... I don't understand how to do it with combinatorics . Can you help me please ? Or do you have another and more efficient way ? This is the problem :A Jar of marble contains 6 yellow and 4 blue marbles, and no other marbles. If four are pulled out of the jar, one after the other, without being replaced, what is the probability that exactly two of the four marbles will be yellow and two blue.
A 1/10 B 1/7 C 1/6 D 3/7 9 9/11 My answer number :
There is 6 possibilities to arrange 2 yellow and 2 blue (let's write YYBB) according to the MISSISSIPPI rule : \(\frac{4 !}{2 x 2}\) = 6
Here are the 6 different possibilities : YYBB, YBYB, YBBY, BYBY, BYYB, BBYY
So now, let's calculate the probabilities :
P (YYBB or YBYB or YBBY or BYBY or BYYB or BBYY ) = P (YYBB) + P(YBYB) + P(YBBY + P(BYBY) + P(BYYB) + P(BBYY ), since the outcomes are all mutually exclusives.
P(YYBB) =\(\frac{6 * 5 * 4 * 3}{10 * 9 * 8 * 7}\) = \(\frac{1}{14}\)
Each expression is equal so : P (YYBB or YBYB or YBBY or BYBY or BYYB or BBYY ) = 6* \(\frac{1}{14}\) =\(\frac{3}{7}\) PROBABILITY: \(\frac{4!}{2!*2!}*\frac{4}{10}*\frac{3}{9}*\frac{6}{8}*\frac{5}{7} =\frac{3}{7}\). COMBINATORICS: \(\frac{C^2_4*C^2_6}{C^4_{10}}=\frac{3}{7}\). Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 16 Mar 2016
Posts: 131
Location: France
GPA: 3.25

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar [#permalink]
Show Tags
03 May 2016, 14:07
thank you ! What is the level of this question ?



Math Expert
Joined: 02 Sep 2009
Posts: 44566

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar [#permalink]
Show Tags
03 May 2016, 14:10



Intern
Joined: 05 Mar 2018
Posts: 20

Re: A jar of marbles contains 6 yellow and 4 blue [#permalink]
Show Tags
11 Apr 2018, 09:46
Guess Strategy ( if time is less for computation )
Consider there were 5 yellow and 5 blue balls , the probality is 50% for each ball getting selected , hence the answer will somewhere hover around 1/2 , D is closer to 1/2 hence Guess D and move on.




Re: A jar of marbles contains 6 yellow and 4 blue
[#permalink]
11 Apr 2018, 09:46






