P3 (10 points). 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 They are withdrawn from the urn, one at a time without replacement. Let X be the number of red balls removed before the first black ball is chosen. Computer E[X]. Hint: Use the trick of indicator random variables. Number the red balls 1, 2, ..., n. Define the indicator random variables Xi, for i = 1, 2, ..., n, by Xi = {1, if red ball i is taken before any black ball is chosen; 0, otherwise. Express X in terms of Xi.