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A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles

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ariellelouise
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A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   Updated on: 23 Feb 2020, 06:24
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A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles are randomly removed from the bag. What is the probability that 3 yellow and 3 blue marbles remain in the bag?

(A) 1/4
(B) 5/14
(C) 1/2
(D) 5/7
(E) 5/8
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B

Originally posted by ariellelouise on 23 Feb 2020, 06:19.
Last edited by Bunuel on 23 Feb 2020, 06:24, edited 1 time in total.
Renamed the topic and edited the question.
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zhanbo
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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   23 Feb 2020, 07:26
(B). This is a combination question.

Pick 2 from 8 without any restrictions: 8X7/2 = 28
To satisfy the requirement of 3 yellow and 3 blue after picking 2 marbles, we can only pick 2 from the 5 blue marbles: 5X4/2=10.

So the answer is: 10/28.
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nerdynerdnerd
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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   23 Feb 2020, 08:11
Quite easily done. Think about rephrasing the problem at hand, if you put your hand in the bag twice to remove 1 marble each time, what is the probability that you will remove a blue ball each time.

Hence the formula is given at:

5/8 X 4/7 = 5/14
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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   23 Feb 2020, 08:31
ariellelouise wrote:
A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles are randomly removed from the bag. What is the probability that 3 yellow and 3 blue marbles remain in the bag?

(A) 1/4
(B) 5/14
(C) 1/2
(D) 5/7
(E) 5/8


Given: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles are randomly removed from the bag.
Asked: What is the probability that 3 yellow and 3 blue marbles remain in the bag?

Total cases of selecting 2 marbles = 8C2 = 28
If 3 yellow and 3 blue marbles remain in the bag, then 2 blue marbles are taken out of 5 blue marbles
Number of favourable cases = 5C2 = 10

Probability = 10/28 = 5/14

IMO B
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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   23 Feb 2020, 08:38
ariellelouise wrote:
A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles are randomly removed from the bag. What is the probability that 3 yellow and 3 blue marbles remain in the bag?

(A) 1/4
(B) 5/14
(C) 1/2
(D) 5/7
(E) 5/8


total marbles = 8
and since 3 yellow and 3 blue marble are to remain so only 2 blue are to be removed
we have
5/8* 4/7 ; 5/14
IMO B
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BrentGMATPrepNow
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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink] New post   23 Feb 2020, 09:56
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ariellelouise wrote:
A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles are randomly removed from the bag. What is the probability that 3 yellow and 3 blue marbles remain in the bag?

(A) 1/4
(B) 5/14
(C) 1/2
(D) 5/7
(E) 5/8


P(3 yellow and 3 blue marbles REMAIN) = P(2 blue marbles are REMOVED)
= P(1st marble is blue AND 2nd marble is blue)
= P(1st marble is blue) x P(2nd marble is blue)
= 5/8 x 4/7
= 20/56
= 5/14

Answer: B

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Re: A bag contains 3 yellow and 5 blue equally sized marbles. Two marbles [#permalink]
23 Feb 2020, 09:56
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