The Monty Hall Problem December 17, 2005
Posted by Sina in : Main , trackbackThe outcome of ths problem is so beautiful that I couldn’t help myself but to post it here and not just on my math page. Here it is:
“You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of the doors and that there are goats behind the other two. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn’t pick to show a goat (because he knows what is behind each door). Then he says that you have one final chance to change your mind before the doors are opened, and asks you if you want to change your mind and pick the other unopened door instead. What do you do?
Using your intuition you might think that there is a 50-50 chance that there is a car behind each door. But according to Marilyn vos Savant you should always change and pick the other door because chances are 2 in 3 that there will be a car behind that door. 92% of the readers wrote in to Marilyn and said she was wrong, many of whom have Ph.D’s in mathematics.”
But Marilyn is right, do you see why? If you’re really curious and want to see why, I posted the solution here (look at all comments, but the final solution is in the last comment I posted).
Amazing, huh?
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