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A box contains red and blue balls only. If there are 8 balls

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A box contains red and blue balls only. If there are 8 balls [#permalink]

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New post 27 Nov 2010, 20:36
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Difficulty:

  55% (hard)

Question Stats:

61% (00:54) correct 39% (00:59) wrong based on 66 sessions

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A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Please explain your appraoch
[Reveal] Spoiler: OA

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Re: Balls in the box [#permalink]

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New post 27 Nov 2010, 21:01
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udaymathapati wrote:
A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?
(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14
(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Please explain your appraoch

Lets say there are R red balls and 8-R blue balls.
S1: P(Both-Red) = \(\frac{R}{8}*\frac{R-1}{7} = \frac{5}{14}\)
so R(R-1) = 5*4, hence R = 5 (considering only positive value). Sufficient

S2: P(Red-Blue) = \(\frac{R}{8}*\frac{8-R}{7} = \frac{15}{56}\)
so R(8-R) = 15, hence R = 5 or 3. Not Sufficient

Answer: A
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Vaibhav

PS: Correct me if I am wrong.

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Re: A box contains red and blue balls only. If there are 8 balls [#permalink]

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New post 30 Sep 2017, 08:30
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Re: A box contains red and blue balls only. If there are 8 balls   [#permalink] 30 Sep 2017, 08:30
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