Some controversy?

[Chainsaw]

You're on a tv show. The prize is a car. To win the car you have to select the box it is hidden behind.

There are 3 boxes. Behind one is the car and behind the other 2 there are goats. You dont want to win the goats.

The host asks you to chose a box. Once you have chosen a box you dont open it straight away. The host then opens one of the other 2 boxes. He will never open a box to reveal the car.

You are now given the option to change your choice of box to the other unopened box or stay with your origional choice.

Is it better to stay with your first answer, change to the other unopened box or wont it make any different which you chose?





I just want to see how many people have heard this before.
Please dont post the answer if you know, lets see what people think.

[LordPhil]

WTF? I was lost from the begining.

[wishy]

Wishy knows the answer, /me is not saying anything tho, although i can demonstrate @ I8

[TommyGun]

hmm.. there's always a trick answer to these...

but surely its a 50/50 choice, so i reckon it won't make any difference.

shoot me

[wishy]

Bang!

Can i tell um? Can i tell um? Please

[LordPhil]

Tell me Wishy, Tell me!

[Chainsaw]

The Answer is........

B. You should change to the other unopened box.

Heres the explanation, I try and do a basic job.

Full problem and explanation here (http://www.math.toronto.edu/mathnet/games/monty.html).

If we take one case, where the player always choses box one. There are 3 combinations for the location of the goats and car. We will play the game twice with each combination. This means that when box 1 is the car, the host will open box 2 on one play, and box 3 on the other play. For the other 2 combinations the host will always reveal the goat. The host never opens the box the player chose.


I will try and demonstrate with the use of a badly contructed diagram.
o=host opens box.
the player always chose box 1 initially.

(Please excuse the dots but forum wont accept whitepace)


...........Box No.......1..............2...............3

............................c...............g(o)..........g
............................c...............g..............g(o)
............................g...............c..............g(o)
............................g...............c..............g(o)
............................g...............g(o)..........c
............................g...............g(o)..........c


As you can see (I hope) when the player is given the choice to chose whether to stick or whether to change, he will have only chosen the car initially 2 out of six times, whereas the other available box will contain the car 4 out of six times.

This means that the player has a 1/3 chance of winning if he stays with his origional choice, but a 2/3 chance of winning if he changes his mind and choses the other available box.

[KermitTheFrag]

But I'd rather have the goat!!!!! *grin*.

[wishy]

We did this in further maths, nobody from the other subjects got it (Physics, Buisness, Computer) they all thought i'd lost it.

[Tom]

OK, Chainsaw, its official...

You have too much time on your hands mateh. :D

[Chainsaw]

What were you doing stats in further maths for wishy?
or were you actually using a stats module as part of it?

I ended up doing Maths (pure with mechanics), Further Maths (further pure with further mechanics....... dont ever do that, I never got rotational motion at variable speed), physics, gen studies and AS- Stats.

[wishy]

I did AS stats in further maths, had a great time, really small group, simular interests, so we got on great, got to know eachother well. Great time, even if i get a U I'll be happy i did it, a course i actually enjoyed, unlike the others which I'm doing for the A levels.