This is a fun assignment to do. In chapter 5 you learned about basic probability and learned about conditional probability. Now, you get to see these two in action. You may have heard of the TV game: Let’s make a Deal. Where at the end of the show, contestants are presented with 3 doors and they are informed that behind one of the doors is a brand new card. So, the contestant chooses one of three doors. Then the game show host (First one was Monty Hall), opens a door and reveals a goat. Then Monty asks if the contestant wants to switch or not. So the question is, what is the probability of winning? Should I stay, or should I switch? What would you do?
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? Think about what you think the answer is: stay or switch?