porbability

[jigar24]

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 then 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 o it is ZERO

(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

[jigar24]

The ANS is (E)

Aren't the statements contradicting each other?: .. What am I missing?

From the question we know that:

w/25 + 5/25 - w/25*5/25 = ? (DeMorgan's Law)

In other words we just have to find the number of white balls in the box

Statement 1

w/25*5/25 = 0 ... Thus w = 0

Statement 2

w/25 - 5/25 = 0.2 ... Thus w = 10

[furtadovinod]

The ANS is (E)

Aren't the statements contradicting each other?: .. What am I missing?

From the question we know that:

w/25 + 5/25 - w/25*5/25 = ? (DeMorgan's Law)

In other words we just have to find the number of white balls in the box

Statement 1

w/25*5/25 = 0 ... Thus w = 0

Statement 2

w/25 - 5/25 = 0.2 ... Thus w = 10

The question is

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 then 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 ZERO

(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

From the question stem we can set up this equation

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

All we can say from the question is that there are 25 balls. We are not told how many of them are of a particular color or how many are even or how many are odd. (Your assumption of 5/25 is therefore incorrect because we cannot assume that only 5 balls are even).

Statement 1: From this we can tell that P(White and Even) = 0.
Tells us nothing about P(White) or P(Even) or P(White) + P(Even)
Therefore, this statement by itself is insufficient.

Statement 2: From this we are told that P(White) - P(Even) = 0.2
Once again insufficient as what we need is P(White), P(Even) and P(White and Even).

Combining Statements 1 and 2: We only know the value of P(White and Even). Given that P(White) - P(Even) = 0.2 does not tell us anything about P(White), or P(Even) or P(White) + P(Even).

Therefore, the answer is E; Both statements are insufficient.

[jigar24]

thanks, i misunderstood the question..

[Ben Ku]

Thanks furtadovinod for a thorough explanation.

jigar24 ... this is how the GMAT trips us up ... by putting information there so that we inadvertently make incorrect assumptions. Here, you're assuming the number of even balls is 5 because they tell you they're numbered from 1-10. So be careful with every word in the question the GMAT poses. Hope that helps!

[jigar24]

yeah.. I make a lot of such silly mistakes.. especially in DS probs.. Thanks a lot.. Will be more attentive..

Cheers,
Jigar

[RonPurewal]

yeah.. I make a lot of such silly mistakes.. especially in DS probs.. Thanks a lot.. Will be more attentive..

Cheers,
Jigar

good luck