The scientist Harry wants to study the lion population in two different areas, Area 1 and Area 2. He assumes that the number of lions, X and Y, in Areas 1 and 2 is Poisson distributed.The ecologist reckons that the expected number of lions is respectively $λ_1 = 3$ in area 1 and $λ_2 = 5$ in area 2
(a) If a lion is in such an area, Harry assumes a probability of 0.4 that it is observed. If in reality there are 5 lions in the area, what is the probability that three of them are observed? What is the expected number of lions observed?
So I have been told that this is binomial distribution problem, is this true? And how is this a binomial problem, and why does the problem talk about Poisson distribution then?