As a successful sales manager at Ford of Damocles, a large auto dealership in Damocles, Ohio, you believe there’s a 30% chance that you’re going to be promoted this week to Assistant VP (Event A1) and a 70% chance that you won’t (Event A2 ). You also believe that if you are going to be promoted, your boss is 80% likely to give you a friendly greeting (Event B) when you arrive at work today. If you’re not going to be promoted, the probability of a friendly greeting drops to 5%. When you arrive at work, your boss gives you a friendly greeting.
a. Use Bayes’ theorem to revise your prior probability that you will be promoted.
b. Show the appropriate probability tree to confrm your answer in part a.