Prob # 20 a) b) c) d) e) f) g) h) i) j) k) 1) Of 20 rats in a cage, 12 are males, 9 are infected with a virus, and 7 are males that are infected with the virus. Let M be the event that a randomly selected rat is male. Let F be the event that a randomly selected rat is female. Let I be the event that a randomly selected rat is infect with the virus. Find P(M). Find P(F). Find P(1). Find P(1 and M). Are the events I and M mutually exclusive? Why or why not? Find P(IM). Is being male independent of being infected? Why or why not? Find P(I and F). Are the events I and F mutually exclusive? Why or why not? Find P(FI) Find P(M and F). Are the events M and F mutually exclusive? Why or why not? Prob # 21 a) b) c) d) e) One card is selected at random from an ordinary deck. The table shows all 52 equally likely outcomes. P(A) P(B) Let A be the event a face card is selected (Jack, Queen, or King). Let B be the event a king is selected. Let C be the event a heart is selected. In parts a) through i), find the probability. Hearts A 2 3 4 5 6 7 8 9 10 JQ K Diamonds A 2 3 4 5 6 7 8 9 10 6789 10 JQ K JQK A 2 3 4 5 A 23 45 678 10 JQ K P(C) P(A or B) P(A and B) Spades Clubs 99