A and B play a series of tennis matches. The probability that A wins any single match in the series is 0.6. The winner of the series is the first player to win either two matches in succession or a total of three matches. Show that the probability

(a) that the series lasts exactly two matches is 0.52,

(b) that the series lasts exactly three matches is 0.24. Calculate the probability that the series lasts exactly four matches. Hence, or otherwise,show that the probability the series last five matches is 0.1152. Calculate the expectation of n, the number of matches in the series. The prize-money involved depends on and is shown in the table below. Prize-money 2 1000 3 4 or 5 1240 1510 Tickets are sold, each of which entitles the purchaser to see the whole series of matches. Given that each ticket costs 5, calculate the number of tickets which must be sold to cover the expected value of the prize-money. (C)