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.
An alternate approach is to TEST CASES.
Let:
W = the total number of white marbles.
E = the total number of even marbles.
WE = the total number of white even marbles.
Statement 1:
Thus, WE = 0.
No way to determine the value of W or E.
INSUFFICIENT.
Statement 2:
Implication:
W-E = (0.2)(25) = 5.
Case 1: W=10, E=5, WE=0
Here, P(W or E) = (10+5)/25 = 15/25 = 3/5.
Case 2: W=11, E=6, WE=0
Here, P(W or E) = (11+6)/25 = 17/25.
Since P(W or E) can be different values, INSUFFICIENT.
Statements combined:
Cases 1 and 2 satisfy both statements.
Since P(W or E) can be different values, INSUFFICIENT.
The correct answer is
E.
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