It can be shown mathematically that the probability of winning with the Stay stragtegy is 1/3, as it is simply your chance of picking the correct door to begin. But what about the Switch strategy? 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.
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When you create output like this, we will often want you to save your results. The simplest way to make a “screen capture” of your results is to use the “Snipping Tool” (see the technology notes in PolyLearn for a couple of other options). To use the Snipping Tool, click on the scissors icon along the bottom toolbar. If it’s not there, select Start > All Programs > Accessories > Snipping Tool. The tool will open with the New button already pressed. Now drag your mouse to select the region you want to copy (just the histogram is fine here). This will display in a preview window. Use ctrl-C/ctrl-V to copy and paste this image from the preview window and into this Word file.
(i) Use the Snipping Tool to take a screen capture of your results (the table and the 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 in your own words what it means to say "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.]
