1. A marketing manager wants to study the effectiveness of online advertisement on social media. For example, Facebook, Twitter, Instagram etc. If a person is exposed to an advertisement, there will be the three outcomes;

P = A person purchases an advertised product.

B = A person only browses an advertised product but does not purchase.

N = A person does not react on an advertisement at all.

We assume that the three outcomes are equally likely. In order to study the effectiveness of advertisements, outcomes of advertisement exposures and search history of advertised products were recorded. Percentages of people that searched the advertised products previously are 70% for purchasers and 50% for people who only browsed products. 20% of people without any reaction to advertisements searched the advertised products previously.

(a) Let S be the statement that a random person exposed to an advertisement searched the advertised product previously. Calculate the posterior probabilities using a Bayes Box. [4 marks]

(b) 200 people were exposed to advertisement on products that they searched previously. How many of them are expected to not purchase? [1 mark]

(c) What is the probability of seeing an advertisement that the advertised product was never searched previously? [2 marks]