Thursday, March 04, 2010

Thursday Riddle : The Monty Hall Problem

This is a riddle based on the old game show Let's Make A Deal. You're the lucky person who gets to try and win the Grand Prize, which is located behind either Door #1, Door #2, or Door #3. There are booby prizes behind the other two doors. . For the sake of this riddle, we'll assume you picked Door #1. The show's emcee, Monty Hall, now opens one of the two other doors (we'll assume here it was Door #2), which always contains one of the booby prizes. He now asks you whether you want to stick with your pick, or switch to the remaining door, which here is Door #3. Statistically speaking, what should you do? . a.) Stick with your original choice. The only reason Monty is making you this offer is because he know you've picked the right door. . b.) Switch to the remaining door. Any genius knows it has a better chance of having the Grand Prize behind it than your door. . c.) It doesn't matter. The odds are the same for either door. Two doors; one prize. The chances are 50:50. What could be simpler? . d.) Consult the pigeons. Everybody knows birds are smarter than humans. . . The correct answer is given in the Comments of this post. Alternatively, you can read the MSNBC article about it here.

1 comment:

terry said...

the correct answer is "b.". the remaining door has twice as good of a chance of containing the Grand Prize as your pick. for an explanation of this, see the MSNBC article.

half-credit for "d.", since the pigeons learned faster in the lab test than the humans did.

FWIW, even though i know the answer, i still have a tough time wrapping my brain around it. the odds may have been 1-in-3 to begin with, but they change when Monty opens the second Door.

but who am I to argue with Marilyn Vos Savant?