Data Sufficiency

Its a problem with two events which can occur simultaneously.

The original question was:
"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."

Now I want to show that the 2 statements both together are insufficient. So let's suppose they are both true.
If the ball is white there are two cases: either the ball is white with an odd number painted on it or the ball is white with an even number painted on it (but we know that the second case is impossible due to the first statmenet.
If the ball has an even number painted on it there are two cases: either the ball is white or it is not, but we know that the first case is impossible due to the first statement. So what the second statement is very saying is "The probability that the ball will be white and will not have an odd number on it minus the probability that the ball will not be white and will have an even number painted on it is 0.2". So Let's look at the table below. I called A the prob. "not white, even number", I called B the probabililty "not white odd number". As you can see the only condition we have is that A+A+0.2+B=1 with 0<=A,B<=1 but there are different several ways to do that: A=0.1, B=0.6 rather than A=0.2, B=0.4 . So they are insufficient.

We have to see if we can find the value of:
P(white or even number) = P(white) + P(even number) - P(white & even number)

Statement (1) says that there is no ball that is white and has an even number printed on it.
It just tells us that P(white & even number) = 0, which is not enough to answer the question.
All we get now is:
P(white or even number) = P(white) + P(even number)
INSUFFICIENT.

Statement (2): P(white) - P(even) = 0.2
INSUFFICIENT.

If we combine the two statements, there is still no way to get the value of 'P(white) + P(even number)'. So, there is no conclusive answer even after combining.

(E) should be correct.

I am not an english native. So I want to ask: does "either white or with an even number painted on it" mean that it can be white or with an even number painted on it but noth both? If so than the formula that you, aneesh.kg have written is wrong:
P(white) + P(even number) - P(white & even number) gives you the probability that the ball is white or has an even number painted on it or both.

simone88 wrote:I am not an english native. So I want to ask: does "either white or with an even number painted on it" mean that it can be white or with an even number painted on it but noth both? If so than the formula that you, aneesh.kg have written is wrong:
P(white) + P(even number) - P(white & even number) gives you the probability that the ball is white or has an even number painted on it or both.

Well what Aneesh has written is correct. There is a flaw in your description. I have highlighted it with red. Pl. delete 'not' and add 'also'.

"either white or with an even number painted on it" mean that it can be white or with an even number painted on it but noth both also?

Simone:
These are mutually inclusive events and for mutually inclusive events such as these,
"either white or with an even number painted on it" means:
P(only white) + P(only even) + P(both white and even)
= P(white) + P(even) - P(both white and even)

(you can see this by drawing Venn-diagrams]

aneesh.kg wrote: P(only white) + P(only even) + P(both white and even)
= P(white) + P(even) - P(both white and even)

Yes, I agree with this formula. Anyway, to be sure that I understood what either or means, let's make an example: If I say that I am either beautiful or tall, then can I be a beautiful and tall guy?

because somebody told me that if I use either...or I am excluding that both cases can happen

By default, I'd be open to the possibility that two events could both happen together, unless the question clearly suggests that the events are mutually exclusive.

For the example stated by you, I'd say that you could be tall and beautiful. (mutually inclusive)
For the example of tossing a coin, the chances of getting a Tail and a Head are 0. (mutually exclusive)

The question at hand (ball problem) was not worded properly. One had to read Statement (1) and assume that it is a case of mutually inclusive events.

Don't worry, the GMAT questions will be leave no room for doubt.