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).