Question

Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue?
(1) There are a total of 24 marbles in the jar, 8 of which are red.
(2) The probability that the marble selected will be white isl

• 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 C Both statements together are sufficient, but neither statement alone is sufficient.

Arithmetic Probability

This problem can be solved by determining the number of marbles in the jar and the number that are blue.

(1) This indicates that there are 24 marbles in the jar and 8 of them are red. The number of marbles that are blue is not known; NOT sufficient.

(2) This indicates neither the number of marbles in the jar nor the number that are blue; NOT sufficient.

Taking (1) and (2) together, there are 24 marbles in the jar, 8 of which are red and $\frac{1}{2}\left(24\right)=12$ of which are white. Then, the number of blue marbles is $24-8-12=4$, and the probability that one marble selected at random will be blue is $\frac{4}{24}=\frac{1}{6}$

The correct answer is C; both statements together are sufficient.