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# If two balls are randomly selected from a green urn contain

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Intern
Joined: 10 Sep 2013
Posts: 27

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Location: India
Concentration: Accounting, Finance
GMAT Date: 10-25-2013
GPA: 3.66
If two balls are randomly selected from a green urn contain [#permalink]

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19 Sep 2013, 22:08
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Difficulty:

15% (low)

Question Stats:

80% (01:05) correct 20% (01:14) wrong based on 113 sessions

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If two balls are randomly selected from a green urn containing 5 black and 5 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?

A.2/9
B.4/9
C.5/9
D.1/3
E.1/9

[Reveal] Spoiler: OA

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Re: If two balls are randomly selected from a green urn contain [#permalink]

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19 Sep 2013, 23:13
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KK23 wrote:
If two balls are randomly selected from a green urn containing 5 black and 5 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?

A.2/9
B.4/9
C.5/9
D.1/3
E.1/9

To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 5/10
Probability(second ball is white) = 4/9
Probability (both balls are white) = (5/10)*(4/9) = 2/9
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Re: If two balls are randomly selected from a green urn contain [#permalink]

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03 Oct 2014, 12:11
Hello from the GMAT Club BumpBot!

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Re: If two balls are randomly selected from a green urn contain [#permalink]

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29 Mar 2017, 21:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If two balls are randomly selected from a green urn contain [#permalink]

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11 Jul 2017, 09:41
VeritasPrepKarishma wrote:
KK23 wrote:
If two balls are randomly selected from a green urn containing 5 black and 5 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?

A.2/9
B.4/9
C.5/9
D.1/3
E.1/9

To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 5/10
Probability(second ball is white) = 4/9
Probability (both balls are white) = (5/10)*(4/9) = 2/9

The other way around, total possibilities would be 10C2 = 45 and the selection that 2 white balls are selected out of 5 white balls would be 5C2 = 10.
So probability = 10/45 = 2/9

Please let me know if this approach is correct

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Re: If two balls are randomly selected from a green urn contain [#permalink]

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11 Jul 2017, 09:46
Your approach is correct, yes - I prefer to solve these problems the way Karishma did above, but I think the method people will find easiest depends on how they've studied probability.
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Re: If two balls are randomly selected from a green urn contain   [#permalink] 11 Jul 2017, 09:46
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