Question

Suppose you are the manager of a company that sells sporting goods in the internet and suppose you know from past experience that 10 per cent of the people that visit your website buy a tennis racket, 20 per cent buy tennis shoes and the probability that someone buys tennis shoes if he/she has bought a tennis racket is 0.4.
a) Define events A and B and write down P(A);P(B) and P( B|A). (2 points) b) Compute, using the Bayes theorem, the probability that a customer buys a tennis racket if he/she has bought tennis shoes; also compute P(A∩B).
c) Are A and B statistically independent?
d) Compute the probability that a customer does not buy a tennis racket, compute the probability that a customer does not buy tennis shoes and compute the probability that a customer buys tennis shoes or a tennis racket (or both).

Answer 1