Solution by simulatio The Monty Hall Problem Theoretical for Staying 33 1/30%-- Theoretical for Switching 66.7 时中M lumber of ga A program monty. c for simulating the generalized Monty Hall Problem was implemented in ANSI-C and is included. Using the program, data was generated for the two following graphs The graph above shows the convergence of the probabilities to the theoretical values for 3 curtains(each set of game was independently run. The graph plots the percentage of winning if the contestant always chooses to stay with the original door versus if the contestant chooses to switch. The graph clearly reaffirms the theoretical result The graph on the next page shows what happens when we increase the number of curtains from 3 to 100. For each value of curtains, 100,000 games were played. The graph also plots the theoretical values as above. The numerical and theoretical values match extremely well Conclusion In conclusion, I'd like to note that the Monty Hall Problem is unintuitive because it is hard to see when information is brought into the problem, i.e. Monty Hall's opening of the curtain causes the conditional probabilities to change. A related problem, the Prisoner's Problem, has the same structure but asks a different question and may be found in [LR94Solution by Simulation 0 20 40 60 80 100 0 100 200 300 400 500 600 700 800 900 1000 Percentage Won ￾ Number of Games The Monty Hall Problem Staying Switching Theoretical for Staying 33 1/3% Theoretical for Switching 66.7 % A program monty.c for simulating the generalized Monty Hall Problem was implemented in ANSI-C and is included. Using the program, data was generated for the two following graphs. The graph above shows the convergence of the probabilities to the theoretical values for 3 curtains (each set of game was independently run.) The graph plots the percentage of winning if the contestant always chooses to stay with the original door versus if the contestant chooses to switch. The graph clearly reaffirms the theoretical result. The graph on the next page shows what happens when we increase the number of curtains from 3 to 100. For each value of curtains, 100,000 games were played. The graph also plots the theoretical values as above. The numerical and theoretical values match extremely well. Conclusion In conclusion, I’d like to note that the Monty Hall Problem is unintuitive because it is hard to see when information is brought into the problem, i.e. Monty Hall’s opening of the curtain causes the conditional probabilities to change. A related problem, the Prisoner’s Problem, has the same structure but asks a different question and may be found in [LR94]. 3