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?
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?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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?
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