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=PROBLEM OF THE WEEK: =

 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. **What is the probability of winning the car if she stays with her first choice? What if she decides to switch?**
 * Let's Make a Deal!**