Math puzzle

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Okay guys and gals...

Hypothetical situation:

You are on a game show. There are 3 closed doors behind which there is:
1 sportscar
2 goats

Doors are A, B, C.

You do not know which item is behind which door, and you cannot see through. And this presumes you are after the sportscar not a goat!

The game show host says you must pick one of the doors to open. For instance, you pick Door B. However it is not opened yet.

Next, the game show host opens one of the other doors to reveal a goat (the game show host knows which doors have goats, he never shows the sportscar to you). In this case, it happens to be Door C.

The game show host asks you if you would like to switch your chosen door to the remaining door (in this case, Door A).

The Question: Is it to your advantage to switch your choice? why?

Guys, if you already know the answer, please do not tell And this question is answered elsewhere on the internet, so don't go looking!! No cheaters!

no goats or sportscars were harmed in the making of this post.

I know.

I know as well.

Plus anybody who has read Mark Haddon's The Curious Incident of the Dog in the Night-Time will know the answer.

I know


or do I??

I guess you'll never know

There is a 50% probability that currently, everyone in this thread knows the answer.

I know!! !

this is called the 'monty hall problem'. wikipedia has an interesting, full article on it with solution if you search it there.

Let's Make a Deal confused the hell out of me the first several times I saw it. I just couldn't understand why the contestants even bothered dressing up and acting stupid.

Now I know it's all just to have fun, hehe.

i know too

I know as well.

Plus anybody who has read Mark Haddon's The Curious Incident of the Dog in the Night-Time will know the answer.

Look, if everybody knows, there's just no fun... :P

I think half of them only have half the answer.

Okay the puzzle has been running for nearly a week now so I think it's time to make sure everyone has got it right:

The answer:
It is advantageous to change your choice.

Why:
The simple way to understand is that, to start, no matter what, you have 2/3 chance of picking a goat. I.e. MORE chance of picking a goat than ANYTHING ELSE. Let's say Door B contains a goat.

Next, the gameshow host opens a door with a goat behind it (Door C). BINGO -- instantly you have a greater chance of picking the third unknown door (Door A) and getting a sportscar. Why? because to start off with you had a 2/3 chance of picking a goat --> then you've just been shown where the other goat is --> therefore you have a 2/3 chance of always getting a sportscar if you change your answer.

It is NOT 50%/50% chances of getting a sportscar. You are 1/3 worse off if you don't change your answer.

As chesirecat says, there's a wikipedia article -- http://en.wikipedia.org/wiki/Monty_Hall_problem

Well worth working out in your own mind :)

Have fun peeps.

Not only is that only half the answer, it's also incorrect.

Some people doesn't accept that answer since you still have two doors and don't know which one contains the car.
So here's another approach:
Just go through all the possibilities and you might see why, more exactly.
At first selection, you will get a goat 2 out of 3 times. If you select a goat and the host opens another door with a goat, and you decide to change, you'll get the car. In the remaining 1 out of 3 times, you'll select the car at first selection, and sadly, switch to the remaining goat.