The Monty Hall Problem (Probability) (1 Viewer)

[Undertoad]

You are on a game show on television. On this game show the idea is to win a car. The game show host shows you three doors. He Says that there is a car behind one of the doors and there are goats behind the other two doors. He asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens one of the doors you didn't pick to show a goat (he knows what is behind each door). Then he says that you have one final chance to change your mind before the doors are opened and you get a car or a goat. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do? And why?

It's not as easy as first seems...

 

[pLuvia]

Err, I'd stick with it lol?

 

[Riviet]

Spoiler

There are three possible scenarios, each with equal probability (1/3):
* The player picks goat number 1. The game host picks the other goat. Switching will win the car.
* The player picks goat number 2. The game host picks the other goat. Switching will win the car.
* The player picks the car. The game host picks either of the two goats. Switching will lose.
Hence, if the player switches, the probability of winning is 2/3!

 

[Mill]

Spoiler

It's quite a confusing problem for most people even after they've seen the answer. It's perhaps a little more obvious if you consider 1000 doors, and the player randomly picks one. The game show host then opens 998 more doors to show goats. Would you swap? Intuitively, I think we all would - even without understanding the probability! The lesson here is to use Intuition. Bad joke - sorry!

 

[Undertoad]

Spoiler

Yea it is more obvious if you think of it in that case and I think most people would swap. The fact that there would be 1000 doors would dramatically reduce the probability of picking the car straight out (1/1000 instead of 1/3) and I think that most people, even if they weren't maths minded would realise that and hence change. Nice way of explaining it.

 

[SeDaTeD]

Spoiler

The show Deal or No Deal uses a similar idea to this, but with varying prize amounts rather than no prizes.

 

[Templar]

Spoiler

For the general n door case of the problem the best solution is to stick with your door until the last two and then switch.

 

[Affinity]

Spoiler

For the general n door case of the problem the best solution is to stick with your door until the last two and then switch.

Hmm.. I think this is wrong

 

[deadnature]

1/2 chance of getting the car - i think 'overthinking' the problem will just get you more stuck i.e. you toss a coin 99 times and every single time the coin lands heads up what is the prob of getting a tails on the 100 time - 1/2. Remember prob= number of favorable outcomes/ number of possible outcomes.

I hate prob. i just don't think it black and white like maths should be...

Que disagreements

 

[Templar]

Hmm.. I think this is wrong

Read the last line.

 

[SeDaTeD]

"Remember prob= number of favorable outcomes/ number of possible outcomes"
only if all outcomes are of equal probability.
And also, the choice of the door the host opens is not random, he knows which doors do or do not contain the car, so he would open an empty one.