Exercise 6. (a) Any of the following events would lead to the 170E instructor having a bad day: A = {one of his cats throws up} (10) B : {he gets a at tire} (11) C' : {the lecture room WIFI doesn't work} (12) You may assume that the events are mutually independent and that P(A) = 0.05, P(B) = 0.01, and P(C) = 0.02. (a) Calculate the probabilities of each of the following: (i) All three bad day events occur. (ii) None of the bad day events occur. (iii) Exactly one of the bad day events occurs. (b) In fact the instructor has three cats (call them cat S, cat R and cat T). And the event described as A above, is really the event that at least one of the three cats throws up, which occurs with probability 0.05. Assuming that the cats throw up or not, independently and all with the same probability, calculate the probability that cat S throws up