## Computer Simulation

The probability of winning with the Stay stragtegy being 1/3 makes sense, because your chance of picking the correct door to begin with is one-out-of-three. Many people believe the probability of winning with the Switch strategy is 0.5 because there are now just two doors. Our simulation tools give us a very easy way to investigate this.

 Return to the Monty Hall applet and use the pull-down menu to now use the "Switch" strategy. Set the number of times to 1000 Uncheck the Animate simulation box Press the Go button

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

(i) Create a screen capture of your results (the table and the Cumulative Win Proportion graph). Based on the 1000 simulated repetitions of playing this game, what is your estimate for the probability of winning the game with the “switch” (i.e, change) strategy?

(j) Does one strategy appear to be better than the other? If so, by a lot or just a little? Justify your answers.

(k) The probability of winning with the “switch” strategy can be shown mathematically to be 2/3. (One way to see this is to recognize that with the “switch” strategy, you only lose when you had picked the correct door in the first place.) Explain what it means to say that the probability of winning equals 2/3.[Hint: Recall our earlier definition of probability. I want an interpretation of this number, not simply an evaluation statement of whether you think it is large or small.]