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# Probability : Random Selection and Conditional Probability

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12. Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen form urn I and put into urn II, and a ball is then randomly selected from urn II. What is
(a) the probability that the ball selected from urn II is white;
(b) the conditional probability that the transferred ball was white, given that a white ball is selected from urn II?

##### Solution Summary

A random selection probability problem is solved.

##### Solution Preview

The answer of (a) is 4/9 and the answer of (b) is 8/9.

(a) When a ball is randomly chosen from urn I to urn II, it can be white or red. Because urn I contains 2 white balls and 4 red balls, the probability that the randomly-chosen ball from urn I is white is 2/(2+4)=1/3. In this ...

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