2021 Jan

Question 3

A drink dispensing machine dispenses either cups of tea or coffee. The number of cups

of tea sold may be assumed to be a Poisson variable with mean of 0.5 cups per 10 minutes

period, while the number of cups of coffee sold may be assumed to be a Poisson variable

with mean of 1.5 cups per 10 minutes period.

(a) Compute the probability that in a given half-hour period. exactly 2 cups of tea.

and 2 cups of coffee are dispensed by the dispensing machine.

(b) Calculate the probability that in a given 45 minutes period, more than 7 drinks

are dispensed by the dispensing machine.

(c) In a 10 minutes period, 3 drinks were dispensed by the dispensing machine.

Calculate the probability that these were all cups of coffee.