43. 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 They are withdrawn from the urn, one at a time and without replacement.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.

Now define the random variables Xi,i = 1,..., n, by Xi =

1, if red ball i is taken before any black ball is chosen 0, otherwise

(a) Express X in terms of the Xi .

(b) Find E[X].