In an urn containing n balls, the ith ball has weight W(i),i = 1,...,n. The    balls are r...

In an urn containing n balls, the ith ball has weight W(i),i = 1,...,n. The    balls are removed without replacement, one at a time, according to the following rule: At each selection, the probability that a given ball in the urn is chosen is equal to its weight divided by the sum of the weights remaining in the urn. For instance, if at some time i1,..., ir is the set of balls remaining in the urn, then the next selection will be ij with probability  j = 1,..., r. Compute the expected number of balls that are withdrawn before ball number 1 is removed.