Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that there are red, white, and blue marbles in a jar. Thus, we can create the following probability equation:
P(red) + P(white) + P(blue) = 1
We must determine the probability of selecting a blue marble. Isolating P(blue) in the above equation, we have:
P(blue) = 1 – [P(red) + P(white)]
Thus, if we can determine the probability of selecting a red marble and the probability of selecting a white marble, we can determine the probability of selecting a blue marble.
Statement One Alone:
There are a total of 24 marbles in the jar, 8 of which are red.
Using the information in statement one, we can determine that P(red) = 8/24 = 1/3. However, we cannot determine the probability of selecting a blue marble since we still don’t know the probability of selecting a white marble. Statement one alone is not sufficient. We can eliminate answer choices A and D.
Statement Two Alone:
The probability that the marble selected will be white is 1/2.
Statement two alone provides no information about the probability of selecting a red marble. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from our two statements, we know that:
P(red) = 1/3 and P(white) = 1/2. Thus, we can determine the probability of selecting a red marble. Although we know the answer will be C, we can complete the problem as follows:
P(blue) = 1 – [P(red) + P(white)]
P(blue) = 1 – [1/3 + 1/2]
P(blue) = 1 – 5/6
P(blue) = 1/6
Answer: C
