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How many red balls are in the barrel?

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How many red balls are in the barrel? [#permalink]

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How many red balls are in the barrel?

(1) The probability of pulling out a red ball after one random selection is 2/7.
(2) The probability of pulling out a white ball after one random selection is 5/7.
[Reveal] Spoiler: OA

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Re: How many red balls are in the barrel? [#permalink]

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New post 29 Mar 2017, 20:26
St1: The probability of pulling out a red ball after one random selection is 2/7. --> R/(Total) = 2x/7x. There can be many values for the number of red balls.
Not Sufficient

St2: The probability of pulling out a white ball after one random selection is 5/7. --> Clearly insufficient as we do not have any info about the red balls.

Combining St1 and St2, we do not know whether the barrel contained only red and white colored balls.
Not Sufficient.

Answer: E
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Re: How many red balls are in the barrel? [#permalink]

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New post 30 Mar 2017, 07:46
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Bunuel wrote:
How many red balls are in the barrel?

(1) The probability of pulling out a red ball after one random selection is 2/7.
(2) The probability of pulling out a white ball after one random selection is 5/7.


Target question: How many red balls are in the barrel?

Statement 1: The probability of pulling out a red ball after one random selection is 2/7.
This tells us that 2/7 of the balls are red.
However, we cannot determine the NUMBER of red balls.
There are several scenarios that satisfy statement 1. Here are two:
Case a: the barrel contains 2 red balls and 5 white balls for a total of 7 balls. Notice that P(select red ball) = 2/7. In this case there are 2 red balls
Case b: the barrel contains 4 red balls and 10 white balls for a total of 14 balls. Notice that P(select red ball) = 4/14 = 2/7. In this case there are 4 red balls
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability of pulling out a white ball after one random selection is 5/7
This just tells us that 5/7 of the balls are white. However, it tells us NOTHING about the red balls. In fact, there might not even be any red balls.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: the barrel contains 2 red balls and 5 white balls for a total of 7 balls. Notice that P(select red ball) = 2/7 AND P(select white ball) = 5/7. In this case there are 2 red balls
Case b: the barrel contains 4 red balls and 10 white balls for a total of 14 balls. Notice that P(select red ball) = 2/7 AND P(select white ball) = 10/14 = 5/7. In this case there are 4 red balls
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
E


Cheers,
Brent
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Re: How many red balls are in the barrel?   [#permalink] 30 Mar 2017, 07:46
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