Quote:
Originally Posted by CalvinandHodges  Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
In other words: What is the probability that if you switch you will win? |
I also think the math supports switching. The point of all of these games is that they are counter-intuitive, our "basic ideas" are being manipulated by the addition of a variable or two.
At first pick, you probably guessed wrong. That's just a fact. You only had a 1/3 probability of being right, 2/3 of being wrong.
You probably have a goat. This is the fact that is missed when, in the 2nd place, you are given a supposedly 50-50 choice.
Then, the FALSE alternative is removed. So, switch. Your odds are slightly BETTER than 1/2 to get the car, rather than lose it, by switching.
Add to it this: if the hosts want to "create a winner" (say its been a bad day for winners), and you get it RIGHT the first time, maybe they just open the door for you and congratulate you on your pick. By giving you a "second choice" they may be hoping you will get the car, but still making a game of it. Can't leave out the "entertainment" factor...
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