We need to find the ratio (no. of blue marbles/total marbles).
(1) 8 are red. So, 16 are either blue or white. This could mean 0 blue, 16 white or any number for blue upto 16, with 16-blue number of whites. Not sufficient.
(2) probability of white is 1/2. So, probability of (blue or red) is 1/2. Now, we don't know the probability of red, so we can't find that of blue. Not sufficient.

(1) and (2) together - probability of white = 1/2. We also know from (1) that there are 24 marbles in all. So, there are 12 white marbles (since 12/24 = 1/2). Out of the remaining, 8 are red, so 4 must be blue. Given this, we can find the probability of blue marbles as 4/24 = 1/6.

Hence, BOTH TOGETHER ARE SUFFICIENT.

Here is a visual that should help.

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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:

RELATED VIDEO

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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. We do not know the number of blue marbles. Not sufficient.
(2) The probability that the marble selected will be white is 1/2. The probability of selecting Red and Blue is 1/2. But we cannot infer the probability that the marble will be blue. Not sufficient.

From 1 and 2, The number of Red and Blue marbles is 12. The number of red marbles is 8, so number of blue marbles is 4. Sufficient.

Hence, answer C.

Probability of drawing a blue ball, P (B) = # of blue balls in the jar/total # of balls in the jar
= n(B)/N

Statement 1: Gives value of N and value of n(R) = # of red balls. However, unless we know n(W) = no. of white balls, we can't calculate n(B) = N - [n(R) + n(W)].
Not sufficient. Reject A, D


Statement 2: Gives us P (W) = 1/2. Unless we know values of n(B) and N, we can't calculate P(B). Not sufficient. Reject B

Statement 1 & 2: This gives us N = 24, n(R) = 8. Also, we can calculate n(W) using P(W) and N as show below:

P(W) = n(W)/N
1/2 = n(W)/24
So, n(W) = 12

Now, N = n(B) + n(R) + n(W)
24 = n (B)+ 8 + 12
So, n(B) = 4

Therefore, P (W) = n(W)/N = 4/25 = 1/6

Sufficient. Mark C

Answer: Option C

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Solution:

Question Stem Analysis:

We need to determine the probability of selecting a blue marble at random, given that the jar has red, white, and blue marbles.

Statement One Alone:


From statement one, we see that 24 - 8 = 16 marbles are either blue or white. However, since we can’t determine the number of blue marbles, we can’t determine the probability of selecting a blue marble. Statement one alone is not sufficient.

Statement Two Alone:


From statement two, we see that the probability of selecting a white marble is 1/2. However, since we can’t determine the number of blue marbles, we can’t determine the probability of selecting a blue marble. Statement two alone is not sufficient.

Statements One and Two Together:


From the two statements, we see that, of the total 24 marbles, 8 of them are red and ½ x 24 = 12 of them are white. Therefore, there must be 24 - 8 - 12 = 4 blue marbles. Hence, the probability of selecting a blue marble at random is 4/24 = 1/6. Both statements together are sufficient.

Answer: C

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