Suppose that there are n identical urns each containing white and black balls. The ith urn, where 1≤i≤n, contains 1 white ball and 2i−1 black balls. You randomly select an urn and then draw one ball at random from it. The ball is white. Let p(n) be the probability that if you replace this ball and again draw a ball at random from the same urn then the ball drawn on the second occasion is also white. Compute n→∞limp(n).
