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white or blue. If one marble is to be selected at random fro

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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white or blue. If one marble is to be selected at random fro

Post Mon Jul 24, 2017 9:24 am
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 is 1/2.

Official Guide question
Answer: C

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Post Mon Jul 24, 2017 9:34 pm
jjjinapinch wrote:
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 is 1/2.

Official Guide question
Answer: C
If we know how many red, white and blue marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

OR

If we know how many blue marbles and the total number of marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

OR

If we know how many red and white marbles and the total number of marbles are there in the jar, we can get the probability that the marble will be blue upon drawing a marble.

Statement 1: There are a total of 24 marbles in the jar, 8 of which are red.

This means that there are 24 - 8 = 16 white and blue marbles; however, we do not know the number of blue marbles. Insufficient.

Statement 2: The probability that the marble selected will be white is 1/2.

Certainly not sufficient as we do not know the number of blue marbles.

Statement 1 & 2:

Say there are b numbers of blue marbles, thus the number of white marbles = 16 - b

=> The probability that the marble selected will be white = (16 - b) / 24 = 1/2

16 - b = 12

b = 4

The probability that the marble selected will be blue = 4/14 = 1/6. Sufficient.

The correct answer: C

Hope this helps!

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Top Reply
Post Mon Jul 24, 2017 10:11 am
jjjinapinch wrote:
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 is 1/2.

Official Guide question
Answer: C
Target question: What is the probability that the marble will be blue?

Given: Each of the marbles in a jar is either red or white or blue.

Statement 1: There are a total of 24 marbles in the jar, 8 of which are red.
There are several scenarios that satisfy statement 1. Here are two:
Case a: there are 8 red marbles, 3 white marbles and 13 blue marbles. In this case, P(marble is blue) = 13/24
Case b: there are 8 red marbles, 2 white marbles and 14 blue marbles. In this case, P(marble is blue) = 14/24
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The probability that the marble selected will be white is 1/2
No information about the red marbles or blue marbles. So, statement 2 is NOT SUFFICIENT

If you're not convinced, consider These two cases, which lead to different answers to the target question:
Case a: there are 8 red marbles, 12 white marbles and 4 blue marbles. Notice that P(white) = 12/24 = 1/2. In this case, P(marble is blue) = 4/24
Case b: there are 11 red marbles, 12 white marbles and 1 blue marble. Notice that P(white) = 12/24 = 1/2. In this case, P(marble is blue) = 1/24
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that there are 24 marbles, and 8 are red
Statement 2 tells us that half the marbles are white. So, 12 of the 24 marbles are white.
If there are 24 marbles, and 8 are red and 12 are white, then the REMAINING 4 marbles must be blue
This means P(marble is blue) = 4/24 = 1/6
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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