Probability Puzzle 2: The Game Show Paradox Let’s say you are a contestant on a

Question

Probability Puzzle 2: The Game Show Paradox

Let’s say you are a contestant on a game show. The host of the show presents you with a choice of three doors, which we will call doors 1, 2, and 3. You do not know what is behind each door, but you do know that behind two of the doors are beat up 1987 Hyundai Excels, and behind one of the doors is a brand new Cadillac Escalade. The cars were placed randomly behind the doors before the show, and the host knows which car is where. The way the game is played out is as follows. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a Hyundai Excel (he will always open one of the remaining doors that has the booby prize), and asks you whether or not you want to change your choice to door #2. What do you tell him?

Explanation / Answer

We should tell him that WE WANT TO SWITCH TO #2. [ANSWER]

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This is because by the time we have chosen a door, we are most probabily wrong (1/3 probability of winning). Hence, it is more probably that the other door is the winning door.

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