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A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar
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03 May 2016, 12:43
Question Stats:
68% (02:33) correct 32% (02:58) wrong based on 95 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 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* \(\frac{1}{14}\) =\(\frac{3}{7}\)
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Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar
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03 May 2016, 12:59
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



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Posts: 52390

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar
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03 May 2016, 13:01
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.
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Joined: 16 Mar 2016
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Location: France
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Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar
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03 May 2016, 13:07
thank you ! What is the level of this question ?



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Joined: 02 Sep 2009
Posts: 52390

Re: A Jar of marble contains 6 yellow and 4 blue marbles, and no other mar
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03 May 2016, 13:10



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Joined: 05 Mar 2018
Posts: 33

Re: A jar of marbles contains 6 yellow and 4 blue
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11 Apr 2018, 08:46
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
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11 Apr 2018, 08:46






