A paint factory uses "agent A" in the paint manufacturing process. There's an average of 3 particles of agent A in a cubic metre of the air emitted during the production process. Calculate the probabilities if this rate is approximated by a Poisson process.
For full marks your answer should be accurate to at least four decimal places.
a) Exactly 5 particles of agent A in 3 cubic metres of air emitted from the factory?
P(x) =