Consider a sample space with ten numbers, S = {1, 2, . . . , 10}. All numbers can be picked with equal probabilities. Let A = {1, 2, 3, 4}, B = {2, 3, 4, 5, 6}, and C = {8, 9, 10}. (a) WhatisAB? WhatisA\B? Whatis(ABC)c? (b) Define D = {2, 3, 4}. What is P (D|A)? What is P (A|D)? Show your work. (c) Suppose I randomly pick two numbers without replacement, and the or- der doesn't matter (e.g., 3 and 4 is the same as 4 and 3). What is the probability that both numbers are greater than 3? Explain. (d) Suppose I randomly pick two numbers with replacement, and the order does matter. What is the probability that both numbers are greater than 3? Explain