Problem 2-Way Cool...Super Awesome... Totally Rad Monty Hall Simulation (8 point

Question

Problem 2-Way Cool...Super Awesome... Totally Rad Monty Hall Simulation (8 points total) In class I showed you a website that simulated the Monty Hall problem (see Lesson 9 notes for details about the problem). This website did not allows us to simulate more than 1000 games at one time. Since "probability" is a LONG-RUN proportion of times an outcome occurs, let's simulate this game for something like 1,000,000! Locate the Monty Hall R Function found on Canvas in the Assignment #3 Link. By double clicking on the link, the file should open automatically in R. Follow the instructions provided within the R file then answer the following questions (4 points) First -run the simulation using both the switch strategy and the stay strategy. It can be shown that the probability of winning if you STAY is 1/3 0.3333 and the probability of winning if you SWITCH is 2/3-0.6667. Why does the R simulation find probabilities for each strategy that are approximately 0.3333 and 0.6667, not exactly 0.3333 and 0.6667? Explain. a. (2 points) The Monty Hall simulation file provides you with a third strategy of randomly deciding to either switch or stay with the door originally selected. What is the probability of winning using this "random" strategy? b. (2 points) Considering the three different strategies, switch, stay or random, which would you choose? In other words, which strategy provides the largest probability of winning the car? c.

Explanation / Answer

b) P( switch)=P( stay)=1/2 because is is randomm

P( Win) = P(Win/Stay)*P(Stay)+P(Win/Switch)*P(Switch)=1/2*1/3+1/2*2/3=1/2

c) Switching provided the largest probability of winning at 2/3

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