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...

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.