65. The number of red balls in an urn that contains n balls is a random variable that is equally likely to be any of the values 0, 1,..., n. That is, P{i red, n − i non-red} =

1 n + 1

, i = 0,..., n The n balls are then randomly removed one at a time. Let Yk denote the number of red balls in the first k selections, k = 1,..., n.

(a) Find P{Yn = j}, j = 0,..., n.

(b) Find P{Yn−1 = j}, j = 0,..., n.

(c) What do you think is the value of P{Yk = j}, j = 0,..., n?