Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors.

1.  The question is, should the contestant switch doors?  Yes or No.

2.  What do you think the probability of winning the car is if she does decides to switch?

3.  What do you think the probability of winning the car is if she stays with her first choice (doesn't switch)?

4.  Review your answer above.  Do you answers to questions 2 and 3 equal one?  Do they coincide with your answer in number 1?  If not, adjust your answers.

5.  Let's find the answers to the above problems using simulation.  In this version, you either win a donkey or money.   Play the game at least 100 times and try to "switch" doors as many times as you as you "do not swtich".  Open:    http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

a.  What is the probability of winning the money if you switch doors?

b.  What is the probability of winning the money if you do not switch doors?

c.  Should the contestant switch doors?

6.  Discuss your results.  Did you guess correctly?  How close were your probabilities to the simulation probabilities.  Are you surprised with the results?

7.  For the mathematical justification visit:  http://mathforum.org/dr.math/faq/faq.monty.hall.html