1) Consider a game where you role three fair dice and count the total. The dice are eight, ten and twelve sided respectively. (a) Write an R function that will compute one round of this game. Have it return the values of the three dice and their total. Store the dice roles by the number of sides of the dice (smallest to largest). (b) Using the code in (a) write a function that will simulate n rounds of the game. (c) Suppose you win another role if the total of the three dice roles is less than or equal to 14. Write an R function that will compute the proportion of roles that meet this criteria after n rounds.
1) Consider a game where you role three fair dice and count the total. The dice are eight, ten and twelve sided respectively. (a) Write an R function that will compute one round of this game. Have it return the values of the three dice and their total. Store the dice roles by the number of sides of the dice (smallest to largest). (b) Using the code in (a) write a function that will simulate n rounds of the game. (c) Suppose you win another role if the total of the three dice roles is less than or equal to 14. Write an R function that will compute the proportion of roles that meet this criteria after n rounds.
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:1) Consider a game where you role three fair dice and count the total. The dice are eight,
ten and twelve sided respectively.
(a) Write an R function that will compute one round of this game. Have it return
the values of the three dice and their total. Store the dice roles by the number of
sides of the dice (smallest to largest).
(b) Using the code in (a) write a function that will simulate n rounds of the game.
(c) Suppose you win another role if the total of the three dice roles is less than or
equal to 14. Write an R function that will compute the proportion of roles that
meet this criteria after n rounds.
(d) Run (c) for n = 1000000. Repeat this five times and look at the results.
(e) What does this tell you about the odds of rolling a total of 14 or less?
(f) Suppose you win $100 if you role triple sevens. Write an R function that will
compute the proportion of roles that meet this criteria after n rounds.
(g) Run (f) for n = 1000000. Repeat this five times and look at the results.
(h) What does this tell you about the odds of rolling triple sevens?
(i) Suppose the game ends if you either role triple sevens or run out of free roles (sum
of dice > 14). Write an R function that returns a 1 if you win and zero otherwise.
(j) Using (i) what do you think are the odds of winning this game?
Submit your R code as ql.R. Also, please label each part (a)-(j) with a comment header
(i.e. # (a)). Use commented text (#) to answer any textual question.
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