Companies that do business over the Internet can often obtain probability information about Web site visitors from previous Web sites visited. For instance, the Q.M. in Action, Internet Marketing, described how clickstream data on Web sites visited could be used in conjunction with a Bayesian updating scheme to determine the probability that a Web site visitor was female. Par Fore created a Web site to market golf equipment and apparel. Management would like a certain offer to appear for female visitors and a different offer to appear for male visitors. A sample of past Web site visits indicates that 60% of the visitors to ParFore.com are male and 40% are female.
a. What is your prior probability that the next visitor to the Web site will be female?
b. Suppose you know that the current visitor previously visited the Dillards Web site and that women are three times as likely to visit this Web site as men. What is your revised probability that the visitor is female? Should you display the offer that has more appeal to female visitors or the one that has more appeal to male visitors?