The Monty Hall Problem
I’m perfectly blown-away by this math puzzle and the solution. If you are familiar with this, just roll your eyes and say ‘obviously’ and leave the rest of us to our thought experiment. Feeling superior because you have read the correct answer beforehand is not grounds for laurels. Only if you can deduce the correct answer, and explain why (remember those notes with the math test answer?) do you you deserve a pat on the back and a position in government.
So here it is. Monty shows us three doors. Behind one is a certificate entitling you to an energy efficient, ergonomic and beautifully designed home. Behind the two other doors are models of that home as doll houses. You must choose one of the three doors. But wait! After you have chosen one door, smiling Monty opens one of the other doors and shows you one of the doll houses. Well duh! He knew which door has the real prize, and whether you chose it or not he knew which remaining door he could open and show a doll’s house.
Now you can choose. Stay with your original choice, or switch to the other unopened door? Don’t read further before making your choice! Common sense would dictate that there is a 50/50 chance that the door you chose has the prize, so it doesn’t matter if you change your mind or not … and mental momentum is likely to make you stick with your original choice, since there is no overwhelming reason to change. Or is there?
Your original choice had a one in three chance of being correct. Monty has kindly shown you one of the wrong choices, and left two others. One is your original 33% chance of being correct — the other? There is a 66% chance that the other has the prize. If you chose correctly to begin with, Monty could choose either door, it makes no difference and doesn’t change the odds. But if you chose wrong (as would happen two out of three times) then Monty must choose the door with no prize, so two out of three times he is showing you where the prize is by not choosing the door it hides behind.