5. As the accounts manager in your company, you classify 78% of your customers as having "good credit" and the rest as having "risky credit" depending on their credit rating. On average, customers in the "risky" category allow their accounts to go overdue 50% of the time whereas those in the "good" category allow their accounts to go overdue only 8% of the time.

Using Bayes Theorem and a tree diagram, answer the questions that follow.

a) What is the probability that an account is overdue?

b) What is the probability that a customer is in the "good credit" category and has an account that is overdue?

c) Given that an account is overdue, what is the probability that it is a customer in the "risky credit" category