question archive In the mid-1600s, a French nobleman (Antoine Gombaud, Chevalier de Méré) frequently gambled using six-sided dice
In the mid-1600s, a French nobleman (Antoine Gombaud, Chevalier de Méré) frequently gambled using six-sided dice
Subject:Computer SciencePrice: Bought3
In the mid-1600s, a French nobleman (Antoine Gombaud, Chevalier de 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 49%.1Write 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: a.(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 problemb.(5 points) Use a main function to control overall program flowc.(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:i.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-modern-probability-theory/, last accessed September 28, 2021 and “de Méré’s Problem,” Wolfram MathWorld, available at http://mathworld.wolfram.com/deMeresProblem.html, last accessed September 28, 2021 for more information.
