Question Three [10 marks] BlackBean Coffee operates a national chain of organic coffee shops providing fair-trade and organically sourced coffee blends. They are looking at launching a new coffee product that uses a revolutionary new roasting technique that they have developed. They expect the market response to be a Event A: Favourable market response , with a large number of sales. Event B: Weak market response , with a small number of sales. Event C: Complete failure of the product with no uptake. Give the unusual nature of this product , they expect probability of Event C:A complete failure to be 0.40. They expect the probability of Events A and B to be equally likely. This is not the first time they have made experimental coffee and in the past they have seen market uptake lead to nationwide television coverage that has been beneficial in advertising the business. Event D: They get television coverage and promotion. Event E: They do not get television coverage and promotion. Past experience has shown that television coverage doesn't occur if the product is a complete failure. Otherwise 1. When there is a favourable market response the probability of TV coverage is 0.2. 2. When there is weak market response the probability of TV coverage is 0.05. Using this information answer the following questions (a) Draw the Probability tree showing the possible events A,B.C,D and E along with the probabilities of A, Band C, the 6 relevant conditional probabilities P(D | A), P(D | B) etc. and the 6 relevant joint probabilities P(DNA), P(DNB) etc. [3 marks] (b) Set out the contingency table with rows for Event A , Event B and Event C and columns for event D and event E. Your table should contain the joint probabilities and the marginal probabilities. [2 marks] (c) Find the probability that we will get television coverage if there is a favourable market response. BBL [1 mark] (d) Find the probability that we will get television coverage before we know the market response. 29 [2 marks] (e) Find the probability that we will receive a favourable market response or receive television coverage , or both? [3 marks] Total marks : 11=3+2+1+2+3