Weekend Brain Teaser

**Kyle123** · 09-08-2012, 04:30 AM

Here's an old one to think over:

You're on a game show and you must choose one of three doors.

You win the prize behind the door of your choosing; behind 1 of the doors is a car, behind the other two are goats.

You choose a door, the game show host (knowing where the car and goats are) then helps you out by opening one of the doors and showing you a goat - he must always show you a goat, it's the rule of the show!

You now have 2 doors remaining, your chosen door and the last remaining door.

The host asks you if you would like to switch your chosen door.

Would you switch or not and why?

**zbor** · 09-08-2012, 04:33 AM

I would switch and I know why... But I won't spoil brain storming for others

**Kyle123** · 09-08-2012, 04:36 AM

I should probably have changed the format, bit easy to google as it is, but googling is no fun

**zbor** · 09-08-2012, 04:42 AM

Actually we had a debate few years ago about it so we discussed it

The main problem was that our question was formed without knowing where the car and goats are part and after that he could't proove his theory wich is 33% in that case

**Kyle123** · 09-08-2012, 04:45 AM

Sorry, I wasn't insinuating that you had googled the answer; I was just saying that keeping the items as they were makes it easy to google.

Indeed, it's all about the order and prior knowledge

**JapanDave** · 09-08-2012, 05:21 AM

Sorry Kyle,

http://www.youtube.com/watch?v=cXqDIFUB7YU

**daddylonglegs** · 09-09-2012, 08:12 AM

As per JapanDave's link this is the "Monty Hall" problem (named after a 1970s US game show host). I have a book called "Understanding Probability" by Henk Tijms (it's very good) and he uses it as an example of how even mathematicians can misunderstand probablility.

In a 1990 magazine article Marilyn vos Savant correctly answered the dilemma, only to find many Ph.D's writing to disagree - see here

**vandan_tanna** · 09-10-2012, 12:59 PM

Note: I haven't followed any of the links provided, so sorry if I am stating something that has already been said:

1. At the start, probabilities are 1/3 for each door. That is simple and needs no explanation. So the odds are 1/3 for you, 2/3 against you.
2. Once the host opens a door with a goat, that 2/3 against you now belongs to just one door. If you switch, 2/3 of the time you will win!

Example: Door 1 has car, 2 and 3 has goat.

1. You pick door #1, host opens door #2, you switch you loose.
2. You pick door #2, host opens door #3, you switch and win
2. You pick door #3, host opens door #2, you switch and win

Now that is statistics. Fate laughs at statistics. In my case, if there is 50/50 chance something can go wrong, 9 out of 10 times, it will.