At a particular spot in a local lake there are on average 25

At a particular spot in a local lake, there are on average 25 fish per cubic meter. If we assume that the probability of finding a fish is the same in this region over all cubic meters of water and the number of fish in any one cubic meter in this region is independent of the number that are in any other cubic meter, what is the probability that we will find exactly 12 fish in the cubic meter we are fishing in?

Solution

probability that we will find the fish exactly 12 = poison distribution can be used

mu = 25

P(x = 12) = e^(-25)*(25)^12/12! = 0.00173 (Ans.)