The Garry oak (Quercus garryana) is a variety of oak tree that is native to the Pacific Northwest. An aerial survey suggests that in densely forested areas the Garry oak follows a Poisson distribution with an average of 4 trees per 1,000 m2 (square meters).

(a) What is the probability that in a densely forested area the size of one hectare (10,000 m2) there is exactly 38 Garry oak trees?

b) What is the probability that in a densely forested area the size of 2,000 m2 there are between 6 and 11 (inclusive) Garry oak trees?

c) In a 3,000 m2 densely forested area, at least 10 Garry oak trees have already been seen. What is the probability that at most 15 Garry oak trees will be seen?

(d) Consider 6 non-overlapping densely forested areas of size 2,000 m2 each. What is the probability that in exactly 4 of these 6 areas there will be at least 10 Garry oaks found