Stone problem

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An urn contains A white stones and B black stones. A second urn contains C white stones and
D black stones. One stone is drawn at random from the first urn and transferred to the second
urn. Then a stone is drawn at random from the second urn. Calculate the probability of each
of the following events.
a. The first stone is white.
b. The first stone is black.
c. The second stone is white, given that the transferred stone was white.
d. The second stone is white, given that the transferred stone was black.

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