In Example 2.45, let and be the probabilities that urn 0 or urn 1 is used in the nth subexperiment..

In Example 2.45, let and be the probabilities that urn 0 or urn 1 is used in the nth subexperiment. (a) Find and (b) Express and in terms of and (c) Evaluate and for (d) Find the solution to the recursion in part b with the initial conditions given in part a. (e) What are the urn probabilities as n approaches infinity?