12. In the school fair there is a horse racing game. The horses are coloured: red, blue and green. If red wins you get £1, if blue wins you get £1.5, and if green wins you get £2. The red horse takes 10 seconds to complete the race, the blue horse takes 9.8 seconds 40% of the time and takes 10.2 seconds 60% of the time. The time taken by the green horse time follows a normal distribution N(11, 1.44). (a) Given this information write out the probability distribution of the winnings. (b) Assuming you want to make an expected profit on each play of the game, what is the minimum price you should charge to play this game? (c) Assuming you want to be 90% confident of making at least £50 total profit across 100 plays, what is the price you should charge per game?