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?
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 ...
A random selection probability problem is solved.