Repeat Problem 3.87 when each of the 3 players selects from his own urn. That is, suppose that there are 3 different urns of 12 balls with 4 white balls in each urn.

An urn contains 12 balls, of which 4 are white. Three players—A, B, and successively C 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b. The balls that are withdrawn are not replaced.

Problem 3.87

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b. The balls that are withdrawn are not replaced;