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Each of the 25 balls in a certain box is either red, blue or

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Each of the 25 balls in a certain box is either red, blue or [#permalink] New post 15 May 2011, 09:31
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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?

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

ii) 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
[Reveal] Spoiler: OA

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Re: Probability - Data Sufficiency [#permalink] New post 15 May 2011, 09:50
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probability of the ball to be white = A
probability of the ball to be an even numbered ball = B

A U B = A + B - (A intersection B)

a. A intersection B = 0. Not sufficient as A and B not given.

b. A-B = 0.2 not sufficient for solving the equation.

a+b

A U B = B+0.2 + B - 0

gives value in terms of B. Hence not sufficient.

E.

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Re: Probability - Data Sufficiency [#permalink] New post 16 May 2011, 12:03
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We can also translate each statement into plain English:

1) There are no white balls with even numbers on them. Therefore, if we can find the chance of white and the chance of even, we can add them without having to worry about overlap. However, we don't have much to go on from this statement alone. If they asked for the chance that the ball was white AND even, clearly this would be sufficient.

2) The chance of white exceeds the chance of even by 20%. This isn't the same as saying 'The chance is 20% greater.' For instance, the chances could be white 50% and even 30%, but not white 12% and even 10%. In any case, we have no idea what the actual numbers are. Insufficient.

1 & 2) We know that the total chance = w + e. Since w = e + .2, we can say that the total chance = 2e + .2. However, since we have no idea what e is, this is insufficient. More simply, we can just say that we don't have an actual number for either probability, so there is no way to add them up.

I hope this helps!

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Re: Probability - Data Sufficiency [#permalink] New post 17 May 2011, 08:17
(1)

White balls don't have any even # on them

P(W) + P(E)

w/25 + e/25

Insufficient

(2)

w/25 - e/25 = 0.2

Insufficient

(1) + (2), Insufficient

Answer - E

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Re: Probability - Data Sufficiency   [#permalink] 17 May 2011, 08:17
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