ISCAM
Lab 0

Definition: The probability of an outcome refers to the long-run proportion of times that the outcome would occur if the random process were repeated a very large number of times under identical conditions. You can approximate a probability by simulating the process many times. Simulation leads to an empirical estimate of the probability, which is the proportion of times that the event occurs in the simulated repetitions of the random process.

• Run each strategy at least 1000 times. (Hint: Uncheck the animate box first. Don't press Reset in between.)

When you create output like this, we will often want you to save your results. 

(e) Take a screen capture of your results (the table and the Cumulative Win Proportion graph) and paste into your lab report.

Based on the simulation results so far, does one strategy appear to be better than the other?

 

(f) Estimate the probability of winning for each strategy, based on your simulation results.

(g) The probability of winning with the “stay” strategy can be shown mathematically to be 1/3. (Your chance of predicting the correct door to begin with.) Explain what it means to say that the probability of winning equals 1/3.[Hint: Use the above definition of probability. I want an interpretation of this number, not simply an evaluation statement of whether you think it is large or small or how it can be calculated.]

 

(h) Many people believe the probability of winning with the Switch strategy is 0.5 because there are just two doors left. Does that appear to be the case?