Search for question

Méré) frequently gambled using six-sided dice. One of his favorite games of chance involved an

attempt to roll at least one "double six" within 24 attempts (or rolls of the 2 dice). He knew the

probability to roll a double six on any given roll of two dice is 1/36 (6 possible outcomes for each

die; 2 dice; 6*6 = 36). He falsely assumed that the probability of rolling double sixes in 24

attempts would be 1/36 24 or approximately 67%. Due to the financial losses he experienced over

time, he determined his probability logic must be false. He subsequently sought expertise from

Blaise Pascal (a contemporary mathematician) to assist him in determining the correct probability

as closer to 4996

Write a "simulation" program that repeats the 24 rolls 10,000 times. Check to see if your simulated

data provides supporting evidence of the 49% probability of rolling double sixes at least once in 24

rolls of 2 dice. Create two separate data files from your simulation. Your program should:

(5 points) Use a "markdown" cell in your Jupyter Notebook to introduce your solution for this

problem and describe any difficulties/issues your team encountered while solving the problem

(5 points) Use a main function to control overall program flow

(15 points) Store the outcome of each pair of dice roll as a .csv file (add text delimiters as

necessary). At a minimum, fields should include:

i Round (1 to 10,000) ii. Roll (1 to 24)

iii. Die-1 (roll of one die 1 to 6) iv. Die-2 (roll of second die 1 to 6)

v. Doubles (1 if result of roll is doubles or 0 if the result is not doubles) vi. Double sixes (1 if result

is double sixes or 0 if the result is not double sixes)

d. (15 points) Store the outcome of each round of 24 rolls as a csv file add text delimiters as

necessary). At a minimum, fields should include:

1. Round (1 to 10,000)

1 See Ma, Dan, "One Gambling Problem that Launched Modern Probability Theory, Introductory

Statistics blog available at https://introductorystats.wordpress.com/2010/11/12/one-gambling-

problem-that-launched-modem-probability-theory/

last accessed September 28, 2021 and "de Mére's Problem, Wolfram MathWorld, available at

http://mathworld.wolfram.com/deMeres Problem.html

last accessed September 28, 2021 for more information.

Last modified: September 27, 2022

Page 5 of 6

ii. Double sixes (True if double sixes occurred at least once during 24 rolls;

otherwise, False)

iii. Winner (House or Gambler). The gambler wins if double sixes are rolled at least

one out of 24 rolls.

iv. Number of Double Sixes Rolled (count of the number of double sixes in the 24

rolls)

e. (25 points) Conduct an analysis of your simulation results and report to the user what you

learned. For this part of the problem, you should use the data files you created in parts (a) and (b) as

input data for your analysis. You should display the results of your analysis on the screen and save

the same output to a .txt file. Some suggestions include:

i. Check to see if your data supports the 49% probability as described above ii. Validation checks to

ensure that the dice are "fair" (i.e., each number 1 to 6 has

equal chance of occurring)

iii. Summary statistics such as the number of times double sixes occurred in 24

rolls, number of doubles rolled in 24 rolls iv. Other interesting statistics

v. Use your creativity here!

f. (5 points) Include a program header and appropriate comments to document your code