The Monty Hall Problem

In honor of his passing, let's discuss the following:

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?

 

I don't need a car.

 

Or a goat.

 

Yes, absolutely, you change your original pick t0 the other available door. It increases your odds of winning the car.

 

It's easier just to go buy a car.

 

My eyes go cross-eyed when we go to bingo and then I scream out BINGO! before Ive even got it.........the old folks get PISSED!! Theres no way in hell I could go on a gameshow.

 

Goats are cool.

 

You switch doors. Learned that on a movie

 

How about I just give you 5oo bucks cash instead right now?

 

I'll take the 500.

 

Doesn't matter. Either I get to drive a new car, or eat well and have some awesome goat cheese.

 

There was a 33 1/3 percent chance that you would pick the door with the car on your original pick.

With the second choice offered, there's a 50 percent chance that you will select the door with the car.

Change your pick.

 

The first pick and the second pick are totally different experiences....no reason to change. Now if he offered 51%+ cash (cost of the car), after showing you one of the doors with the goats...take the cash.

 

Is the goat rocket powered?

 

Uh, what? At stage 2 you have already picked one option on a coin flip. Why bother changing.

(minus of course the psychology factor of the game show host knowing the doors options and his actions tipping a favor one way or the other [tells], if showing a non winning door isn't standard practice).

It doesn't matter if you change your pick or not since it's a coin toss. I'd keep my pick only to remove the embarrassment if the car was in door 1, and I had changed from winning to a losing door because of effectively worthless information of the 3rd door (and irrelevant in second round) being a loser.

 

Actually, I was wrong: changing doors improves your odds to 2/3. If your original pick offered 1/3 odds, the remaining door MUST contain the rest of the possibilities, therefore it's 2/3.

Mind f**k, I know, but true.

 

No I wouldn't change my choice. Especially since the host knows what is behind the door and suggested #2. He could be paid to suggest a door with a less expensive prize, but that's only speculation. As mentionned above, it's a 50/50 guess then.