Hi all!
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.
a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.
E is the right answer, I guessed and was right, but if you could provide me an explanation, I would be thankful!
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Probability with balls
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Target question: What is the value of P(white or even)?szDave wrote:Hi all!
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.
To solve this, we need 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
Still need P(white), and we need P(even)
INSUFFICIENT
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)
INSUFFICIENT
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
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Brent
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Anurag@Gurome
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Already discussed here: https://www.beatthegmat.com/probability- ... 18795.htmlszDave wrote:Hi all!
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.
a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.
E is the right answer, I guessed and was right, but if you could provide me an explanation, I would be thankful!
Anurag Mairal, Ph.D., MBA
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