Use the preceding meal to choose each transition probability

Mr Ong chooses either a Beef Combo Meal or a Chicken Combo Meal at a fast food restaurant. On his first visit, the probability of beef is 0.8. Thereafter, the probability of beef is 0.6 if he chose beef on the previous visit and 0.7 otherwise.

(i) Show that the probability of beef on each of the first three consecutive visits is 0.288.1 mark

(ii) Find the probability of exactly one beef meal in those visits.2 marks

(iii) Given exactly two chicken meals in those visits, find the probability that the second visit’s meal was beef.2 marks