1. (a) 1/5  (b) 3/5 (c) being in a band
2. (a) 77 (b) 79.5 (c) 95 (d) 365 (e) 19.1
3. (a) 0.3 (b) no (c) no (d) A and B are disjoint (e) B and C are independent (f) 1/7 (g) 1/4
4. (a) P(X = x) = (1/3) * (2/3)^(x-1) for x = 1, 2, ...  (b) 3 (c) P(Y = y) = (1/3) * (2/3)^(y/50 - 2) for y = 100, 150, 200, ... (d) 200 (e) 25/54