The Monty Hall Problem

[JGL53]

Logic is a subtopic of philosophy, is it not?

OK, then, for everyone's enjoyment and edification I present the Monty Hall Problem, aka "The Three Door Problem".

Don't cheat. Read the problem as presented above the line and give your answer - THEN read the explanation of the correct answer below the line.

Good luck.


Math Forum: Ask Dr. Math FAQ: The Monty Hall Problem

 

[DeathMagus]

Spoiler: Switching doors will provide a win 2/3 of the time. Keeping the same door will only cause a win 1/3 of the time. This occurs because keeping the same door means that your odds of being right are the odds of picking one door out of three. Switching doors inverts the odds - if you had chosen wrong, the new door would be right, and if you were right, the new door would be wrong. Since you are more likely to be wrong at first, switching doors inverts your odds, and your new door is more likely to be right.

It's a rather counter-intuitive problem.

 

[JGL53]

Spoiler: Switching doors will provide a win 2/3 of the time. Keeping the same door will only cause a win 1/3 of the time. This occurs because keeping the same door means that your odds of being right are the odds of picking one door out of three. Switching doors inverts the odds - if you had chosen wrong, the new door would be right, and if you were right, the new door would be wrong. Since you are more likely to be wrong at first, switching doors inverts your odds, and your new door is more likely to be right.

It's a rather counter-intuitive problem.

So tell me - was this your first encounter with the MHP?

Did you immediately figure out the correct answer?

If so, then you are indeed smarter than the average bear.

Though I still think you need to look into that humility thingie.

 

[DeathMagus]

So tell me - was this your first encounter with the MHP?

Not at all. I've actually studied the problem twice for different reasons in various CS courses.

Did you immediately figure out the correct answer?

Nope - Like I mentioned, it's counter-intuitive. I had to play out a scenario or two to establish the pattern.

If so, then you are indeed smarter than the average bear.

I doubt I'm smarter than the average human, however.

Though I still think you need to look into that humility thingie.

How do you mean?