Last Updated on May 6, 2023
GMAT OFFICIAL GUIDE DS
Solution:
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.
Answer: E
