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Probability (Marbles in a bag)

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by ashfu2002 » Tue Apr 03, 2012 9:22 am
A bag contains some red and some blue marbles.How many red marbles are in the bag?

(1) If two marbles are selected from the bag, the probability of selecting one red and one blue marble is 1/4

(2) There are a total of 8 marbles in the bag.

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by Bill@VeritasPrep » Tue Apr 03, 2012 9:48 am
1) There are two ways of getting one blue and one red, each of which has the same probability:

B-R
R-B

Since the total probability is 1/4, P(B-R)=1/8 and P(R-B)=1/8. If we have 7 red and 1 blue, then P(R-B) = 7/8 * 1/7 = 7/56 = 1/8. P(B-R) would have the same probability for a total of 1/4. However, we can also arrive at the same probability if we have 7 blue and 1 red. Insufficient.

2) R + B = 8. There are many possible combinations of red and blue marbles. 1 and 7, 2 and 6, and so on. Insufficient.

When put together, we still have the same possibilities we had in Statement 1, so we still cannot answer.
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