Terry holds 12 cards, each of which is red, white, green, or blue. If

We are given that Terry has 12 total cards. The cards are colored red, white, green, or blue. We need to determine whether the probability of selecting a red or a white card is less than ½. Remember, since we are determining the probability of selecting a red or a white card, we must add the probabilities.

Is P(red card) + P(white card) < ½?

Since the sum of all probabilities in a sample set is equal to 1, we also know that:

P(red card) + P(white card) + P(blue card) + P(green card) = 1

P(red card) + P(white card) = 1 – [P(blue card) + P(green card)]

Thus, if we can determine the sum of the probabilities of selecting a red card and of selecting a white card OR the sum of the probabilities of selecting a blue card and of selecting a green card, we also could determine the probability of selecting a red or white card.

Statement One Alone:

The probability that the person will select a blue card is 1/3.

Since we don’t know the probability of selecting a green card, we cannot determine:

1 – [P(blue card) + P(green card)] OR

P(red card) + P(white card)

Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The probability that the person will select a red card is 1/6.

Since we don’t know the probability of selecting a white card, we cannot determine:

P(red card) + P(white card)

Thus, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using both statements together we know the following:

P(red card) = 1/6

P(blue card) = 1/3

Substituting this into our two expressions we have:

P(red card) + P(white card) = 1/6 + P(white card) = ?

1 – [1/3 + P(green card)] = ?

We see that we still do not have enough information to determine whether the probability of selecting a red card or a white card is less than ½.

The answer is E.