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?
This solution solves several probability problems related to shopping and purchases.