Companies that do business over the Internet can often obtain probability information about Web site visitors from previous Web sites visited. The article "Internet Marketing" (Interfaces, March/April 2001) described how click stream data on Web sites visited could be used in conjunction with a Bayesian updating scheme to determine the gender of a Web site visitor. 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. From a sample of past Web site visits, management learned that 60% of the visitors to ParFore.com are male and 40% are female.
a. What is the prior probability that the next visitor to the Web site will be female?
b. Suppose you know that the current visitor to ParFore.com previously visited the Dillard's Web site, and that women are three times as likely to visit the Dillard's Web site as men. What is the revised probability that the current visitor to ParFore.com is female? Should you display the offer that appeals more to female visitors or the one that appeals more to male visitors?