Question

A box contains only Red, White & Blue stones. If a stone is randomly selected from the box, what is the probability that the stone will be either white or blue?
I. The probability that the stone will be blue is $\frac{1}{5}.$
II. The probability that the stone will be red is $\frac{1}{3}.$

• A. If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
• B. If the question can be answered by using either statement alone.
• C. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. If the question cannot be answered even by using both the statements together.

Answer 1

The correct option is A If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

From statement (I), only the probability that the stone will be white or red can be determined. Therefore, statement (I) alone is not sufficient. From statement
(II), the probability that the stone will be red is $\frac{1}{3}.$
Note that the probability that the stone will be either white or blue is the same as the probability that it will not be red, which is $1-\frac{1}{3}=\frac{2}{3}.$ Thus, only statement (II) alone is sufficient.