Getting your goat up.

Sean · Guest

Here's an old riddle and I'm sure someone is going to answer it straight away.
You're on a quiz show and you've been given the opportunity to win a car. The host shows you three doors and tells you that behind two of the doors is a goat, and behind the third door is a car. Now pick a door. You pick a door and your host immediately opens a different door to display a goat. He now asks you if you want to change your mind and opt for the other unopened door (instead of the one you originally choose). Should you change your mind? does it make any difference?

Guest · Posted: Fri Feb 03, 2006 4:08 pm Post subject:

You should change your mind becuase chances are you picked a goat(1 out of 3), Since the host always chooses one with a goat, then you should know which two doors have goats know and which one has the car. this would be the one you did not pick. and since this works only when you pick the wrong door (2/3)

BobaFunk · New Member Joined: 06 Aug 2009 Posts: 28

ahhh...the Monty Hall problem

the answer is right, once you choose a door, there is a 1/3 probability of of a car behind the door. when the host knowingly opens a different door to reveal a goat, the probability of your door containing a car is still 1/3, while the probability of the car being behind the other door is 2/3.

ex. three doors, three people, three possibilities, three switches.

everyone selects door one.
a 1=c 2=g 3=g
b 1=g 2=c 3=g
c 1=g 2=g 3=c

after selecting, the host opens a door other than door 1. in case a, it doesn't matter, yet in cases b and c, he has to open the only other door with a goat. so, if everyone at thins point switched, then only player a would lose, players 2 and 3 will both win.
thus, selecting to switch doors will result in a 2/3 probability that you will win the car.