Sunday, January 16, 2005

The Monty Hall Conundrum

I've seen some recent discussion on this issue. This is a logic & mathematics problem. Most people, including some professional mathematicians, get it wrong.

Here's the set-up:

You are on "Let's Make a Deal." Monty Hall shows you three doors and tells you that behind one of the doors, there is placed a brand new car (or a large sum of cash). The other two doors conceal either an empty space or some sort of "Booby Prize."

Let's number the doors, 1, 2, & 3. After you pick your door, Monty decides (out of the goodness of his heart) to show you what is behind one of the other two doors. Obviously, the door that Monty reveals is empty or has a "Booby Prize." Monty then offers you the opportunity to switch to the remaining unchosen and unrevealed door.

Should you?

Does it matter?

Many folks come to the conclusion that it makes no difference because once Monty reveals the one "wrong" door, the odds shift to 50/50. Well, that would be true if no choice had been made prior to the reveal, so why isn't it true after the reveal?

When you made your initial choice, you had a 1 in 3 chance of being correct. You had a 2 in 3 chance of being wrong. After the reveal, that fact does not change. So, you should switch because based on statistics and odds, switching makes it twice as likely that you will win the good prize.

Still doubting?

Try this Simulation. NOTE: It is Java.

2 comments:

tubadave said...

When staying, I was 11 out of 30.

When switching, I was 20 out of 30.

Absolutely fascinating stuff. Never would have thought that way myself, initially. Probability and odds and things like that have never been a strong suit of mine.

Moose said...

So, I'm traveling along in my 1974 Ford Pinto(Yes, I really drove one, it was silver!) and I am rear ended. This causes the gas tank to explode throwing me instantly to a speed faster than light. Since it's nighttime, I flip on my headlights to see where I am going as I travel through Hyperspace. So the question is, do my headlights work?