Probability and Statistics for Engineering and the Sciences (with Student Suite Online)

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Winter, 2008 Monday, Jan. 14 Stat 321 – Lecture 4 Probability (2.1) Example 1 (“Monty Hall” Problem): Suppose that on a game show money is hidden behind one door, while pigs are hidden behind two other doors. A contestant picks a door, and then the host reveals what’s behind a different door that he knows to have a pig. Then the host asks whether the contestant prefers to stick with the original door or switch to the remaining door. (a) Prediction : Do you think the probability of winning is different between the “stay” and “switch” strategies? Explain. (b) Investigate these strategies by playing the game a total of 20 times, 10 with each strategy, using the site: http://www.shodor.org/interactivate/activities/AdvancedMontyHall/ (Click on a door to start the game; then after the host reveals a pig either click on the same door again (“Stay”) or click on the remaining door (“Switch”). Then click on “Reset Doors.”) Won with switching: Won with staying: Lost with switching: Lost with staying: (c) In what proportion of games employing the “stay” strategy did the contestant win? What was this proportion for the “switch” strategy? Does one strategy appear to be superior to the other?
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