In: Statistics and Probability
Adam and Beth are two salespeople at a car dealership. Daily, their boss decides to give a bonus to whoever sells the first car of the day. Assume one of the two will eventually sell a car on any given day. They will alternate serving customers (thus, only one of them is serving a customer at any given time). Suppose there is a 25% chance Adam makes a sale to any customer, there is a 35% chance Beth makes a sale to any customer, and all attempts to sell a car to any customer are independent from one another. It is Thursday morning. Beth desperately wants to go skiing on Saturday but needs at least one bonus to pay for the trip. Thus, she has two days to get her bonus. If Adam and Beth alternate daily who gets the first customer of the day what is the probability that Beth can go skiing