83. An urn contains n balls, with ball i having weight wi , i = 1, . . . , n. The balls are withdrawn from the urn one at a time according to the following scheme: When S is the set of balls that remains, ball i, i ∈ S, is the next ball withdrawn with probability wi/



j∈S wj . Find the expected number of balls that are withdrawn before ball i, i = 1, . . . , n.