Suppose n balls are thrown into n labeled bins one at a time, where n is a positive even integer. (a) what is the probability that exactly k balls land in the first bin, where k is an integer 0 ≤ k ≤ n? (b) what is the probability p that at least half of the balls land in the first bin? (you may leave your answer as a summation.) (c) using the union bound, give a simple upper bound, in terms of p, on the probability that some bin contains at least half of the balls. (d) what is the probability, in terms of p, that at least half of the balls land in the first bin, or at least half of the balls land in the second bin?