A garage has three cars available for daily hire. Calculate the following probabilities if the variable is a Poisson variable with a mean of 2: 

(a) Find the probability that on a given day that exactly none, one, two, and three cars will be hired, and determine the mean number of cars hired per day; 

(b) The charge of hire of a car is £25 per day and the total outgoings per car, irrespective of whether or not it is hired, are £5 per day.

Determine the expected daily profit from hiring these three cars.