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Alex75PAris
Joined: 16 Mar 2016
Last visit: 08 Mar 2017
Posts: 100
Location: France
Schools: Marshall '19 Darden '19 HKUST '19 Anderson '19
GMAT 1: 660 Q47 V33
GPA: 3.25
03 May 2016, 13:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
74% (02:22) correct
26%
(02:43)
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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
E. 9/11
A. 1/10
B. 1/7
C. 1/6
D. 3/7
E. 9/11
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* \(\frac{1}{14}\) =\(\frac{3}{7}\)
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* \(\frac{1}{14}\) =\(\frac{3}{7}\)
03 May 2016, 14:01
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Alex75PAris
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.
03 May 2016, 13:59
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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
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
