There are three horses in a race. Historical records show that the time it takes

Question

There are three horses in a race. Historical records show that the time it takes each horse to complete a similar race is Normally distributed with a mean and standard distribution given in the table below (all numbers are in minutes). Simulate 1,000 races using Excel and answer the questions. Make sure you explain in your write up what each column of your spreadsheet stands for and how you obtained each column from the other data. Submit your excel file. What proportion of the time will each horse win? What proportion of the time will the horses arrive in order: horse 1 then horse 2 then horse 3? Suppose you can place only one of the following $10 bets or choose to not bet anything: Pick one horse and double your money if that horse wins the race, lose your money otherwise. Triple your money if horses arrive in order 1 then 2 then 3, lose your money otherwise. What should you do to maximize the money you have after the race? Why? If you decide to bet, give the expected value of your winnings (i.e. how much total money you have in average after the race).

Explanation / Answer

I have hidden the middle cells, not feasible to paste entire cells

(a) Proportion will change each time, because we are using random numbers to simulate, but based on above data:

Horse 1: 65.8 %

Horse 2: 28.3 %

Horse 3: 5.9 %

b) 56.8 % the order of arrival will be horse 1, then 2, then 3

c) To maximise the money, one should bet on the second option i.e. horse 1, then 2, then 3

In the above case, betting $ 10,000 will yield 56,800 * 3 = $ 17,040

Mean Std dev Horse 1 Horse 2 Horse 3 Winning time Winning Horse Horse 1, 2, 3 Horse 1 0.87 0.17 0.649338 0.971345 1.334336 0.649338 Horse 1 Yes Horse 2 0.95 0.06 0.725172 0.994005 1.183523 0.725172 Horse 1 Yes Horse 3 1.1 0.14 0.749204 0.9745 1.129172 0.749204 Horse 1 Yes 1.13827 0.888389 1.116416 0.888389 Horse 2 False 1.046334 0.836197 1.169707 0.836197 Horse 2 False 1.09772 0.93951 1.144928 0.93951 Horse 2 False 0.874306 0.945072 1.120937 0.874306 Horse 1 Yes 0.409446 0.867187 1.095756 0.409446 Horse 1 Yes 0.703411 0.871368 1.000605 0.703411 Horse 1 Yes 0.669339 0.91329 1.004928 0.669339 Horse 1 Yes 0.74358 0.976445 1.05744 0.74358 Horse 1 Yes 0.974636 0.852125 1.150461 0.852125 Horse 2 False Horse 1 658 568 Horse 2 283 Horse 3 59

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