For (5)-(8) Suppose you pick a number at random from 1 to 100. Let A be the event that the number chosen is even. Let B be the event that the number chosen is prime. It may be helpful to remember that the prime numbers frorn 1 to 100 are 2,3,5, 7, 11, 13, 17, 19, 23,29,31, 37,41, 43,47, 53,59, 61,67, 71, 73, 19, 83,89, 97 (5} (Basic Probability) What are the following probabilities? PM) = ms) = (6} (Mutual Exclusivity) What is the following probability? P(A and B) = Are A and B mutually exclusive? Why or why not? (7} (Independence) What are the following probabilities? PldlB) = P(B|A) = Are A and B independent? Why or why not? (8} (Binomial Probability) Now suppose you pick a number at random from 1 to 10!] ten times. What is the probability that half of the numbers you pick are prime? You need to show your work for this one