Question

         ParFore created a website to market golf equipment and golf apparel. Management would

like a special pop-up offer to appear for female website visitors and a different special

pop-up offer to appear for male website visitors. From a sample of past website visitors,

ParFore’s management learned that 60% of the visitors are male and 40% are female.

a. What is the probability that a current visitor to the website is female? In other words what is P(F)?

b. Suppose 30% of ParFore’s female visitors previously visited the Dillard’s Department

     Store website and 10% of ParFore’s male visitors previously visited the Dillard’s

     Department Store website. If the current visitor to ParFore’s website previously

     visited the Dillard’s website, what is the revised probability that the current visitor is

     female? Should the ParFore’s website display the special offer that appeals to female

     visitors or the special offer that appeals to male visitors?

Use Bayes Theorem below to answer this question

    Where: P(M) = .60, P(D/F)=0.30 and P(D/M)=0.10

Answer 1

a)

It is given that 40% are female so

P(F) = 0.40

and

P(M) = 0.60

b)

Let D shows the event that visitors previously visited the Dillard’s Department Store website.So we have

P(D |F) = 0.30, P(D|M) = 0.10

Using Baye's theorem the revised probability that the current visitor is female given that  the current visitor to ParFore’s website previously visited the Dillard’s website is

P(F|D) = P(D|F)P(F) / [ P(D|M)P(M) + P(D|F)P(F) ] = [ 0.30 * 0.40 ] / [ 0.30 *0.40 + 0.10 * 0.60] = 0.12 / [ 0.12 + 0.06 ] = 0.6667

Answer: 0.6667

--------------------------

P(M|D) = P(D|M)P(M) / [ P(D|M)P(M) + P(D|F)P(F) ] = [ 0..10 * 0.60 ] / [ 0.30 *0.40 + 0.10 * 0.60] = 0.06 / [ 0.12 + 0.06 ] = 0.3333

Since revised probability that the current visitor is female is greater than revised probability that the current visitor is male so the ParFore’s website should display the special offer that appeals to female visitors.