Discuss the below:
Each Saturday a shopper visits one of three possible stores. She goes to Store A with probability ½, to Store B with probability ¼, and to Store C with probability ¼. If she goes to Store A there is a 60% chance that she will make a purchase. The corresponding figures for Stores B and C are 20% and 40% respectively. (i) What is the probability that on a given Saturday she will make a purchase? (ii) What is the probability she makes a purchase on at least two out of three consecutive Saturdays? (iii) What is the probability that if she makes a purchase on at least two out of three consecutive Saturdays then she has visited all three stores? (iv) Her friend has a probability of 1/3 of visiting Store A, Store B or Store C on any Saturday, but, once a store has been visited, has the same chances as she does of making a purchase (60% in Store A, 20% in Store B, and 40% in Store C). If he has made a purchase on at least two out of three consecutive Saturdays, what is the probability he has visited all three stores?