Problem 5. There was an old television show called Let\'s Make a Deal, whose ori
ID: 3041172 • Letter: P
Question
Problem 5. There was an old television show called Let's Make a Deal, whose original host was named Monty Hall. The set-up is as follows. You are on a game show and you are given the choice of three doors. Behind one door is a car, behind the others are goats. You pick a door, and the host, who knows what is behind the doors, opens another door (not your pick) which has a goat behind it. Then he asks you if you want to change your original pick. The question we ask you is, 7s it to your advantage to switch your choice? Hint: Compute the probability of getting the car if you switch, and the probability of getting the car if you do not switch, respectively. See which one has higher probability?)Explanation / Answer
When three choices of doors are given, the probability of winning car = 1/3
If switch is not made, the probability of winning will not change and hence, the chance of winning the car is 1/3
But when asked if you want to change pick, you have two chose only from one of the two doors. Then if you change your pick, your probability of winning is 1/2, because you are picking from only 2 options.
So, it is an advantage if you switch your choice.