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 A_{1}), 20 (event A_{2}) or 25 (event A_{3}) times a year. The probability of A_{2} is the same as the probability A_{1} and the probability of A_{3} is half of A_{1}.
(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(A_{1}|B)? Determine P(A_{2}|B) and P(A_{3}|B).