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.

Target question: What is the value of P(white or even)?

To solve this, we'll use the fact that P(A or B) = P(A) + P(B) - P(A & B)
So, P(white or even) = P(white) + P(even) - P(white & even)

Statement 1: P(white & even) = 0
We can add this to our probability equation to get: P(white or even) = P(white) + P(even) - 0
Since we don't know the value of P(white) and P(even), we cannot determine the value of P(white or even)
NOT SUFFICIENT

Statement 2: P(white) - P(even)= 0.2
We have no idea about the sum of P(white) and P(even), and we don't know the value of P(white & even)
NOT SUFFICIENT

Statements 1 and 2 combined:
Given P(white) - P(even)= 0.2 does not tell us the individual values of P(white) and P(even), and it doesn't tell us the value of P(white) + P(even).

So, since we can't determine the value of P(white) + P(even) - P(white & even), the statements combined are NOT SUFFICIENT.

Answer: E

Cheers,
Brent

hoppycat wrote:I'm getting murdered by probability questions. Maybe its because I prefer using the counting strategy and I thought you can usually use either strategy but it seems that this doesn't work a lot of times. Can we use counting to solve this?

For probability problems involving a small set, I often count rather than using a formula. In this problem, we need to recognize from the question stem that a ball could either be white, have an even number on it, or both. Essentially, we need to know exactly how many of each ball we have, and which numbers are painted on which. From there, we can absolutely just count.

(1) This tells us that there are no balls that are BOTH even and white. But we still have no idea how many out of 25 are white, and how many are even. Insufficient.

(2) This one is going to be harder to count, because it's giving us a DIFFERENCE between probabilities, and not an actual number. But we can test some out:

Scenario 1:
15/25 white balls (p = 0.6), 10/25 evens (p = 0.4). Overall probability of white or even = 25/25 = 1.0

Scenario 2:
10 white (p = 0.4), 5 even (p = 0.2). Overall probability of white or even = 15/25 = 0.6.

Two different answers to the question --> not sufficient.

(1 & 2) Both of the scenarios we tested for statement 2 fit statement 1, so putting the statements together does not give us additional information.

The answer is E.