91Ó°ÊÓ

An urn contains 12 balls, of which 4 are white. Three players \(-A, B,\) and \(C-\) successively draw from the urn, \(A\) first, then \(B\), then \(C\), then \(A\), and so on. The winner is the first one to draw a white ball. Find the probability of winning for each player if (a) each ball is replaced after it is drawn; (b) the balls that are withdrawn are not replaced.

In Laplace's rule of succession (Example \(5 \mathrm{e}\) ), are the outcomes of the successive flips independent? Explain.