Summit Projects provides marketing services and website management for many companies that specialize in outdoor products and services (www.summitprojects.com). To understand customer Web behavior, the company experiments with different offers and website design. The results of such experiments can help to maximize the probability that customers purchase products during a visit to a website. Possible actions by the website include offering the customer an instant discount, offering the customer free shipping, or doing nothing. A recent experiment found that customers make purchases 6% of the time when offered the instant discount, 5% when offered free shipping and 2% when no special offer was given. Suppose 20% of the customers are offered the discount and an additional 30% are offered free shipping.
a) Construct a probability tree for this experiment.
b) What percent of customers who visit the site made a purchase?
c) Given that a customer made a purchase, what is the probability that they were offered free shipping?