An urn contains n m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to n, and define the random variables Xi , i = 1,n by

Xi =1 if red ball i is taken before any black ball is chosen

Xi =0 Otherwise

Required:

a. Express X in terms of the Xi.

b. Find E[X].