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Probability

by Deepthi Subbu » Fri Jan 07, 2011 1:38 am
A bowl contains 50 marbles. What is the probability that a blue or red marble is selected ?

1. The probability that a blue marble is selected is 3/10
2. There are 20 red marbles in the bowl .

When a question wants us to find the probability of any one colored marble or the occurrence of say both blue or red colored marble , should we assume that the bowl may contain other colored marbles also or should we assume that the bowl just has the colored marbles that are mentioned in the question?

Case 1 : Both statements are necessary

Case 2 : Statement (1) is sufficient .
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by Anurag@Gurome » Fri Jan 07, 2011 2:30 am
Deepthi Subbu wrote:A bowl contains 50 marbles. What is the probability that a blue or red marble is selected ?

1. The probability that a blue marble is selected is 3/10
2. There are 20 red marbles in the bowl
Say the number of blue marbles = B and number of red marbles = R
Hence, required probability = (B + R)/50 = (B/50) + (R/50)

(B/50) = Probability of picking a blue marble
(R/50) = Probability of picking a red marble

Statement 1: The probability that a blue marble is selected is 3/10
Hence, (B/50) = 3/10
But we don't about the red ones.

Not sufficient

Statement 2: There are 20 red marbles in the bowl
Hence, (R/50) = 2/5
But we don't know about the blue ones.

Not sufficient

1 & 2 Together: We have both the information.
Required probability = (3/10) + (2/5) = 7/10

Sufficient.

The correct answer is C.

Note: We don't know whether there are other colored marbles or not. Thus we can't assume there are only red and blue marbles.
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by GMATGuruNY » Fri Jan 07, 2011 6:40 am
Deepthi Subbu wrote:A bowl contains 50 marbles. What is the probability that a blue or red marble is selected ?

1. The probability that a blue marble is selected is 3/10
2. There are 20 red marbles in the bowl .

When a question wants us to find the probability of any one colored marble or the occurrence of say both blue or red colored marble , should we assume that the bowl may contain other colored marbles also or should we assume that the bowl just has the colored marbles that are mentioned in the question?

Case 1 : Both statements are necessary

Case 2 : Statement (1) is sufficient .
The problem itself makes it clear that blue and red are not the only colors. Otherwise, the two statements would contradict each other: statement 1 would say that P(B) = 3/10 and P(R) = 7/10, while statement 2 would say that P(B) = 3/5 and P(R) = 2/5. On the GMAT, the two statements will never give contradictory information.
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