A box contains 2n balls of n different colors, with 2 of each color. Balls are picked at random from the box with replacement until two balls of the same color have appeared, Let X be the number of draws made.
a) Find a formula for P(X > k), k = 2, 3, . . .
b) Assuming n is large, use an exponential approximation to find a formula for k in terms of n such that P(X > k) is approximately 1/2. Evaluate k for n equal to one million.