abhi332 wrote: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.
We are given that there are 25 balls in a box and each one is either red, blue, or white and has a number from 1 to 10 painted on it. We need to determine the probability of selecting a white ball or an even-numbered ball.
Since each ball is colored and has a number painted on it, selecting a ball with a number or color is not mutually exclusive. Thus, to determine the probability of selecting a white or even ball we use the following formula:
P(white or even ball) = P(white ball) + P(even ball) - P(white and even ball)
Statement One Alone:
The probability that the ball will both be white and have an even number painted on it is 0.
Using the information in statement one, we know that P(white and even ball) = 0. However, we still cannot determine the probability of selecting a white or even ball. We can eliminate answer choices A and D.
Statement Two Alone:
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.
Statement two does not provide enough information to determine the probability of selecting a white or even ball. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two we still only know the following:
P(white or even ball) = P(white ball) + P(even ball) - P(white and even ball)
P(white or even ball) = P(white ball) + P(even ball) - 0
Without knowing the sum of P(white ball) and P(even ball), we cannot answer the question.
Answer:
E
