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Two urns, named A and B, contain balls. Urn A contains 10 balls numbered 1-10, and urn B contains 25 balls numbered 1-25. An experiment is performed, in which an urn is chosen at random, and then the ball is chosen from the urn. Suppose that the ball chosen has the number 5. What is the probability that the ball came from urn A?

This is a practice exam, so the exact answer is not as important as the proper solution.

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Applying Bayes' theorem:

$$P(A|5) = {P(5|A)P(A) \over {P(5|A)P(A) + P(5|B)P(B)}} = {0.1\times0.5 \over {0.1\times0.5 + 0.04\times0.5}} = {5 \over 7}$$

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