RunningWithTheDevil.com created a web site to market running shoes and other run
ID: 3071359 • Letter: R
Question
RunningWithTheDevil.com created a web site to market running shoes and other running apparel. Management would like a special pop-up offer to appear for female web-site visitors and a different special pop-up offer to appear for male web-site visitors. From a sample of past web-site visitors, RunningWithTheDevil’s management learns that 59% of the visitors are male and 41% are female.
(a) What is the probability that a current visitor to the web site is female? (b) Suppose that 30% of RunningWithTheDevil’s female visitors previously visited LetsRun.com and 10% of male customers previously visited LetsRun.com. If the current visitor to RunningWithTheDevil’s web site previously visited LetsRun.com, what is the revised probability that the current visitor is female? If needed, round your answer to three decimal digits. Should the RunningWithTheDevil’s web site display the special offer that appeals to female visitors or the special offer that appeals to male visitors? RunningWithTheDevil should/should not display the special offer that appeals to female visitors because it is more/less that this visitor is female than male.Explanation / Answer
a) P(current visitor is female) = 0.41
b) P(female | visited LetsRun) = P(female and visited LetsRun) | P(visited LetsRun) [Baye's Theorem]
= 0.41x0.3 / (0.41x0.3 + 0.59x0.10)
= 0.676
RunningWithTheDevil should not display the special offer that appeals to female visitors because it is less chance that this visitor is female than male.
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