A call centre receives calls from customers that are dealt with by agents. Records indicate that 4.2% of customers are not satisfied with the agent and ask to speak with a supervisor. The supervisor is able to resolve the issue 43% of the time so that the customer ends up satisfied. When the customers who have not requested to speak with a supervisor finish speaking with the agent, they are transferred to an automated system that asks whether they are satisfied with the service; 79% of them say yes.

a) Draw a probability tree for the above situation.

b) What is the probability that a customer will end up satisfied?

c) Which method of probability assessment has been used?

d) Which of the probabilities are conditional?

e) What is the probability that a customer who ended up satisfied spoke with a supervisor?