Tuesday, April 15, 2008

The Monty Hall Problem



Monty Hall wants to make a deal. He asks you to choose one of three doors. Behind one door there is a brand new car! Behind the other two doors are goats.

After you have chosen your door, Monty Hall opens one of the doors with a goat behind it. He then asks you if you are going to stick with your first door choice or if you'd like to switch to the remaining door. What do you do?

Well, you might think, "There are only two doors left, so I have a 50/50 chance of winning. I'll just stick with my first choice."

Well, I'm afraid you are wrong. In fact, there is a 66% chance that the car is behind the other door. YOU SHOULD ALWAYS SWITCH.

It's pretty counterintuitive, eh? This video clip might help:




7 comments:

Dave said...

Great post, It really makes you think.

que rediculo! said...

totally counterintuitive. but makes sense when i thought about it. what is this clip from?

Jay said...

I'm not sure where that clip is from, but it did the best job of explaining the concept quickly.

SuiginChou said...

It's from the CBS show "Numbers." I've never watched a full episode, but I understand that:
a) it's filmed at a fictional analogue to Caltech and
b) the star is Bernard from The Santa Clause

I tried submitting a reply earlier but it looks like it got lost in the mail. Basically, I shook my fist at you because you got me hooked on Wikipedia's statistics and probability riddle pages and I spent a good 90 minutes or so reading them thoroughly and sharing with others.

SuiginChou said...

I have been replicating riddles from Professor Layton & the Curious Village for a bright young man of 23 at medical school to solve and he's been doing remarkably well on them, solving puzzles that took me 10-15 minutes in as little as 2 minutes. I showed him the Bertrand Russel box problem (presented as a coin problem) and he solved it, I shit you not, in 10 seconds after I quit talking -- and only because he was chalking things out on the board to hold a conversation with me and not just blurt out the answer immediately. Some people are just gifted like that, I guess. :)

que rediculo! said...

oh yeah!THAT'S where i've seen that guy before!

Jay said...

I was surprised Sam solved the Monty Hall problem right away --but I think he knew something was up.