BrainLab 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.
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) = 13/24Case b: there are 8 red marbles, 2 white marbles and 14 blue marbles. In this case,
P(marble is blue) = 14/24Since 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 1/2No 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) = 4/24Case 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) = 1/24Since 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 = 1/6Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
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