Question

A search engine company has recorded the following information about the effectiveness of their advertising for a certain product: the chance of user clicking on the product’s ad appearing on the side banner during each search is 1/50, the chance of user clicking on the product’s ad site appearing within the search results is 1/5, while the chance that they click on both is 1/100. Of the users that clicked on the product’s ad site, 20% then made a purchase, and of the users that did not click on the product’s ad site only 2% made a purchase. Calculate the chance of a user making a purchase.

Answer 1

let A,B and C are event of a person r clicking on the product’s ad appearing on the side banner , user clicking on the product’s ad site appearing within the search results and making a purchase respectively

from given data": P(A )=1/50 ; P(B) =1/5 ; P(A n B) =1/100 ; P(C| A u B) =0.20 and P(C| (A u B)^c) =0.02

P(A u B) =P(A)+P(B)-P(A n B) =1/50+1/5-1/100 =0.21

P((Au B)^c) =1-P(A u B) =1-0.21 =0.79

chance of a user making a purchase =P(C )=P( A u B)*P(C|AuB)+P((A u B)^c)*P(C|(A u B)^c)

=0.21*0.2+0.79*0.02 =0.0578