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# A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar

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Manager
Joined: 16 Mar 2016
Posts: 129
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar  [#permalink]

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03 May 2016, 13:43
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:34) correct 31% (03:03) wrong based on 88 sessions

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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

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* $$\frac{1}{14}$$ =$$\frac{3}{7}$$
Manager
Joined: 12 Jun 2015
Posts: 79
Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar  [#permalink]

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03 May 2016, 13:59
3
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: 50000
Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar  [#permalink]

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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

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:

$$\frac{C^2_4*C^2_6}{C^4_{10}}=\frac{3}{7}$$.

_________________
Manager
Joined: 16 Mar 2016
Posts: 129
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar  [#permalink]

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03 May 2016, 14:07
thank you ! What is the level of this question ?
Math Expert
Joined: 02 Sep 2009
Posts: 50000
Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar  [#permalink]

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03 May 2016, 14:10
Alex75PAris wrote:
thank you ! What is the level of this question ?

________________
~600.
_________________
Intern
Joined: 05 Mar 2018
Posts: 32
Re: A jar of marbles contains 6 yellow and 4 blue  [#permalink]

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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 &nbs [#permalink] 11 Apr 2018, 09:46
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