Question

Terry holds 12 cards, each of which is red, white, green,or blue. If a person is to select a card randomly from the cards Terry is holding, is the probability less than $\frac{1}{2}$ that the card selected will be either red or white?
(1) The probability that the person will select a blue card is $\frac{1}{3}$.
(2) The probability that the person will select a red card is $\frac{1}{6}$

• 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 E Statements (1) and (2) together are not sufficient.

We have to determine whether the number of cards that are red or white is less than .

1. It is given that the probability is that the selected card will be blue. This means that of the cards are blue. However, there is no information about how many of the $8$ remaining cards are red, how many are white, or how many are green. Thus, this is not sufficient.
2. It is given that the probability is that the selected card will be red. This means that of the cards are red. However, there is no information about how many of the $10$ remaining cards are white, how many are blue, or how many are green.

• Taking (1) and (2) together, there are $4$ blue cards and $2$ red cards. However, there is no information about how many of the $6$ remaining cards are white or how many are green. So, statements (1) and (2) together are not sufficient.