The joy of the Poisson process is that it is ENTIRELY scalable.
"Ships pass a bird sanctuary at a Poisson rate of one per hour."
This is a Poisson process with , referring to ships per day.
"Twenty percent of the ships are oil tankers."
24*0.2 = 4.8
This is a Poisson process with , referring to oil tankers per day.
"1. What is the probability that at least one oil tanker will pass during 24 hours."
1 - P(0) = ??
"2. If 30 ships have past by in one day, what is the probability that 6 of them were oil tankers."
This is a very odd question. It seems to have little to do with whether or not we have a Poisson process. I'm thinking a binomial model would be more appropriate.
p(oil tanker) = 0.2 = p
p(not oil tanker) = 0.8 = q = 1-p
What is the complete term with in it?
I suppose, since 30 is a relatively large number, that some other approximation might be appropriate. The binomial is simple enough in this case that playing with other defininitions may be off the mark.