a) A coin is tossed twice. Calculate the probability of each of the following occurring, commenting briefly on the basis of your calculation:
A head on the first toss;
A tail on the second toss, given that the first toss was a head;
Two tails;
A tail on the first toss and a head on the second;
A tail on the first and a head on the second, or a head on the first and a tail on the second;
At least one head on the two tosses.
Do you think the Poisson distribution, which assumes independent arrivals, is a good estimation of arrival rates in the following queuing systems? Explain your reasoning in each case:
University cafeteria or coffee bar;
Hairdresser's shop;
Hardware store;
Dentist's surgery;
University lecture;
Movie cinema.
Why is a different queuing model needed if the population of potential customers for a system is limited rather than unlimited? Use examples of real or hypothetical systems to illustrate your answer.