4. Summit Projects provides marketing services and website management for many companies that specialize in outdoor products and services. 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 reperiment 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 the were offered free shipping? Summit Projects performed another experiment in which they tested three website designs to see which one would lead to the highest probability of purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. d. Construct a probability tree for this experiment. e. What percent of customers that a randomly selected customer was sent to design C? f. Given that a customer made a purchase, what is the probability that the customer had been sent to design C