# maths problem

• Oct 19th 2006, 01:01 AM
bssm
maths problem
Ok well i was watching this show on telly the other night and on of the guys did a maths problem. im trying to show this to my mates because it was pretty amazing. the problem is i can't remember how he explained it works. it wasn't so much a problem as a fact. it was...
if there are 3 doors, behind 1 is a car, behind the other 2 is a dud prize...obviously you want the car. so you pick the door you think it is behind. then one of the other doors is opened and it is a dud prize. So the car is either behind your door or the other. Do you change your answer? on the show it turned out that there is more probability of getting the car if the answer is change but i can't seem to remember or figure out how this is possible.
So could someone please explain this to me or is not true?
Thanks.
• Oct 19th 2006, 01:55 AM
JakeD
Quote:

Originally Posted by bssm
Ok well i was watching this show on telly the other night and on of the guys did a maths problem. im trying to show this to my mates because it was pretty amazing. the problem is i can't remember how he explained it works. it wasn't so much a problem as a fact. it was...
if there are 3 doors, behind 1 is a car, behind the other 2 is a dud prize...obviously you want the car. so you pick the door you think it is behind. then one of the other doors is opened and it is a dud prize. So the car is either behind your door or the other. Do you change your answer? on the show it turned out that there is more probability of getting the car if the answer is change but i can't seem to remember or figure out how this is possible.
So could someone please explain this to me or is not true?
Thanks.

This is the Monty Hall Problem. This Wikipedia page gives a lot of different ways to look at it and understand it. Here is the graphic for the decision tree approach. By always switching, the constestant gets the car 2 out of 3 times.

• Oct 19th 2006, 04:41 AM
ThePerfectHacker
One thing that makes me angry about this problem is that people thing that there is a debate and some people say the probability is 1/2.

Anyway, here is my explanation I posted on this forum some time ago.....

You are using the strategy that you will switch....
If you pick a bad door, then you win!! How? If you pick a bad door, two doors remain, good and bad. Certainly the bad is open and the good remains. So when you switch you get the good door. What is the probability of picking a bad door? Simple, 2/3 so the answer is 2/3.

Look at it in reverse....
If you pick the good door, then you lose!! How? If you pick the good door, two doors remain, bad and bad. Certainly the bad is open and the other bad remains. So when you switch you get the bad door and lose. What is the probability of picking the good door? Simple, 1/3 so the probability that you will lose on this strategy is 1/3, that is the probability that you will win is 2/3.