Each of the 25 balls in a certain box is either red, blue, : GMAT Data Sufficiency (DS)
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# Each of the 25 balls in a certain box is either red, blue,

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Each of the 25 balls in a certain box is either red, blue, [#permalink]

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26 Mar 2010, 14:14
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Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

(1) The probability that the ball will both be white and have an even number painted on it is 0

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2

OPEN DISCUSSION OF THIS QUESTION IS HERE: each-of-the-25-balls-in-a-certain-box-is-either-red-blue-or-63290.html
[Reveal] Spoiler: OA
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26 Mar 2010, 14:55
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changhiskhan wrote:
Each of the 25 balls in a certain box is either red, blue, or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

1) The probability that the ball will both be white and have an even number painted on it is 0.
2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2.

P(White or Even) = P(White) + P(Even) - P(White & Even)

st 1) P(White & Even) = 0 .. still dont know individual probabilities . Not sufficient
st 2) P(White) - P(Even) = 0.2
.. still dont know abouit the combined probability and also individual probabilities. Not sufficient

combinging also we cannot figure out P(White) + P(Even) as we cannot find out the number of white balls or the number of even balls

E
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Re: Each of the 25 balls in a certain box is either red, blue, [#permalink]

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27 Mar 2010, 08:29
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changhiskhan wrote:
Each of the 25 balls in a certain box is either red, blue, or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

1) The probability that the ball will both be white and have an even number painted on it is 0.
2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2.

It has to be E.
1: p(W & E) = 0
to get p(W or E) = p(w) + p(E) cant find individual probability hence insufficient.
2: p(W) - p(E) = 0.2 cant find individual probability hence insufficient.
Combining, also we cant find anything more hence E
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24 Jul 2014, 14:53
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Re: Each of the 25 balls in a certain box is either red, blue, [#permalink]

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24 Jul 2014, 22:57
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Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

Probability ball: white - $$P(W)$$;
Probability ball: even - $$P(E)$$;
Probability ball: white and even - $$P(W&E)$$.

Probability ball picked being white or even: $$P(WorE)=P(W)+P(E)-P(W&E)$$.

(1) The probability that the ball will both be white and have an even number painted on it is 0 --> $$P(W&E)=0$$ (no white ball with even number) --> $$P(WorE)=P(W)+P(E)-0$$. Not sufficient

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2 --> $$P(W)-P(E)=0.2$$, multiple values are possible for $$P(W)$$ and $$P(E)$$ (0.6 and 0.4 OR 0.4 and 0.2). Can not determine $$P(WorE)$$.

(1)+(2) $$P(W&E)=0$$ and $$P(W)-P(E)=0.2$$ --> $$P(WorE)=2P(E)+0.2$$ --> multiple answers are possible, for instance: if $$P(E)=0.4$$ (10 even balls) then $$P(WorE)=1$$ BUT if $$P(E)=0.2$$ (5 even balls) then $$P(WorE)=0.6$$. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: each-of-the-25-balls-in-a-certain-box-is-either-red-blue-or-63290.html
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Re: Each of the 25 balls in a certain box is either red, blue,   [#permalink] 24 Jul 2014, 22:57
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