The occurrence of bushfires in the Port Stephens area may be modelled by a Poisson process. The average occurrences of bushfires n is assumed to be either 15 (event A1), 20 (event A2) or 25 (event A3) times a year. The probability of A2 is the same as the probability A1 and the probability of A3 is half of A1.
(a) Determine the probability that there will be 20 occurrences of bushfire in the next year.
(b) If there are exactly 20 bushfires in the next year (event B), what will be P(A1|B)? Determine P(A2|B) and P(A3|B).