Question

A small online retailer sells three products: Product A, Product B, and Product C. A study of the purchasing history of their customers reveals the following: No customers purchased both Product A and Product B 1.6 times as many customers purchased Product A as Product B 55% of customers purchased Product C 13% of customers purchased only Product C The event that a customer purchased A is independent of the event that . . they purchased C they purchased C Calculate the probability that a randomly selected customer purchased exactly The event that a customer purchased B is independent of the event that one of the products 0.4736 0.3600 0.4452 0.3884 O 0.4168

Answer 1

here P(A u B u C)=1

P(A)=1.6*P(B)

P(A n B)=0

P(A n C)=P(A)*P(C) ;

P(B n C)=P(B)*P(C)

P(C)=0.55

P(C)-P(C n A)-P(C nB)+P(A n B nC) =0.13

0.55-0.55*P(A)-0.55*P(B)+0=0.13

0.55*2.6*P(B)=0.55-0.13

P(B)=0.2937

P(A)=1.6*0.2937=0.4699

therefore P(exactly one product)=P(A)+P(B)+P(C)-2*P(A n B)-2*P(B n C)-2*P(A n C)+3*P(A n B nC)

=0.4699+0.2937+0.55-2*0-2*0.4699*0.55-2*0.2937*0.55+3*0=0.4736