Question

A box contains only red chips, white chips, and blue chips. If a chip is randomly selected from the box, what is the probability that the chip will be either white or blue?
(1) The probability that the chip will be blue is $\frac{1}{5}$
(2) The probability that the chip will be red is $\frac{1}{3}$

• 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.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

1. Since the probability of drawing a blue chip is known, the probability of drawing a chip that is not blue (in other words, a red or white chip) can also be found. However, the probability of drawing a white or blue chip cannot be determined from this information; NOT sufficient.
2. The probability that the chip will be either white or blue is the same as the probability that it will NOT be red. Thus, the probability is ; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient.