Another Puzzle

Top Hat · Sep 16, 2005

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?

Jayne · Sep 16, 2005

No i'd take the goat :lol: Good for keeping grass short, never have to mow again, well at least until it snuffs it.

Jayne

daveashton · Sep 16, 2005

No its a 50 % chance of a goat or a car.

SillyJokes · Sep 16, 2005

Both wrong - you'd be a fool not to switch.

SuffolkDesigns · Sep 17, 2005

Top Hat said:
Behind one door is a car, behind the others, goats. You pick a door, say number 1,

Of course you don't switch

Behind one door is a car
Behind 3 door is a goat
so, there must be a goat behind 2 door as well

SillyJokes · Sep 17, 2005

No, with the first choise you had a one in three chance of getting the car.

now the game is squewed.

You know that one of the two remaining doors has a goat but the chances are better that it is in the one you didn't pick.

SuffolkDesigns · Sep 17, 2005

SillyJokes said:
but the chances are better that it is in the one you didn't pick.

And in real life we know this still remains true after you change your mind, it will still be behind the door that you didn't choose......

daveashton · Sep 17, 2005

You know that one of the two remaining doors has a goat but the chances are better that it is in the one you didn't pick.

Sorry how do you work that out.

There are 2 doors left

1 has a goat
1 has a car

Odds 50 : 50 so it make do difference is you keep the door or swop it.

:?

Top Hat · Sep 17, 2005

daveashton said:
Odds 50 : 50 so it make do difference is you keep the door or swop it.

When you pick the 1st door the odds are 1 : 3 you are right.
And 2 : 3 that its one of the other doors

The host then opens one of the other doors, remember he knows where the prize is and will always show you a loosing door.

Your door still has odds of 1 : 3, the other unopened door has odds of 2 : 3, so you're best to switch.

Its a lovely counterintuitive problem.

Marina Stone · Sep 17, 2005

Sorry how do you work that out.

There are 2 doors left

1 has a goat
1 has a car

Odds 50 : 50 so it make do difference is you keep the door or swop it.

I'm with you on this one, as long as the goat doesn't have green eyes!

Marina

SuffolkDesigns · Sep 17, 2005

But wouldn't you be p****d off if you switched and was wrong

Always stick to your original decision in cases like this

daveashton · Sep 17, 2005

I would be pissed off to be on the game show in the first place. These people always have naff jobs an earn very little money.

epiphany · Sep 17, 2005

I don't get your maths Top hat

Before you pick each door has a 1/3 chance of being the car

After the goats are revealed behind door three; door 1 and 2's probability alters to a chance of 50/50 each of having the car behind them.

Top Hat · Sep 17, 2005

Odds at the begining is 1:3 behind each door, agree?

You pick a door, the odds of it being one of the other doors is 2 : 3.

So the host open a loosing other door, the prize does not move.

The odds of it being one of the other doors is still 2 : 3, but now there is only 1 other door.

So its best to switch.

Becomes a bit clearer if there are 100 doors, and the host opens 98 loosing doors.

daveashton · Sep 17, 2005

this sorry is getting daft.

Top click your odds are wrong

if there are 2 doors left and 1 is a car and the the other is goat the odds are not 2: 3 but evens

i.e. 50 50 chance, remember to take the other door off you sum as well as the goat!

Top Hat · Sep 17, 2005

daveashton said:
this sorry is getting daft.

Top click your odds are wrong

if there are 2 doors left and 1 is a car and the the other is goat the odds are not 2: 3 but evens

i.e. 50 50 chance, remember to take the other door off you sum as well as the goat!

This is a great puzzle.

always causes problems.

When the host opens the door he is giving you a clue, he knows it is a loosing door. The odds for the other reaming door, therefore equals the odds for the 2 original doors, so switching you have a 2:3 chance of winning. (interestingly, if he opens a random door, and its a loosing door, the odds are even)

Have a google for Monty hall dilemma, and you'll find lots of simulators.

daveashton · Sep 17, 2005

sorry your maths is wrong and all you can go on is facts not conjecture

2 doors left

1 prize=

50:50

Rob Holmes · Sep 17, 2005

Find a good use for a goat (i.e. sell it to a curry house) and at least whatever door you choose you'll be pleased to get something from it.

Top Hat · Sep 17, 2005

daveashton said:
sorry your maths is wrong and all you can go on is facts not conjecture

2 doors left

1 prize=

50:50

But its your maths that is wrong

have a go with some cards and some paper, or write a simulator

Rob Holmes · Sep 17, 2005

Both your maths is wrong - theres a prize behind each door. 1 door a car, 1 door a goat.

Rob

Jayne · Sep 17, 2005

Matrixx said:
Find a good use for a goat (i.e. sell it to a curry house) and at least whatever door you choose you'll be pleased to get something from it.

Yuck! Goat curry.

I agree with the above, except the curry bit

Jayne

DuaneJackson · Sep 17, 2005

Saw this in the book "Curious Incident of the Dog in the night time".

the logic there convinced me it was best to switch. My bro-in-law strongly disagrees though.

Cornish Steve · Sep 18, 2005

I'm in the President's Club at Newark airport trying to understand this puzzle. At last, I think I understand.

Let's call the three doors A, B, and C. There's a 1 in 3 chance that the car is behind door A, 1 in 3 for door B, and one in 3 for door C.

The contestant selects door A. There's a 1 in 3 chance that the car is behind this door. There's a 2 in 3 chance, however, that it's behind one of the other doors.

Wanting to help, the game show host will always open a door with a goat. If the car is behind door B, he'll open door C. If the car is behind door C, he'll open door B. If the car is behind door A, it doesn't matter which door he opens.

At this point, there's a 1 in 3 chance that the car is behind door A and a 2 in 3 chance that it's behind door B or door C. However, one of those two doors is open, and there stands a goat! With this new information, there's a 1 in 3 chance that the car is behind door A and a 2 in 3 chance that it's behind the unopened door - B or C.

The contestant should switch!

chris1317 · Sep 19, 2005

Heres the maths

http://www2.sjsu.edu/faculty/watkins/mhall.htm

Heres a page where you can download a simulator to test it for yourself. I didnt believe it for a start either and thought it was nonsense but understand it now.

http://www.grand-illusions.com/monty.htm

Chris.

SuffolkDesigns · Sep 19, 2005

What happens if you already have a car and really want to win a goat ?

Top Hat · Sep 20, 2005

vshosting said:
What happens if you already have a car and really want to win a goat ?

If you want the goat, you should stick, as you have a 2 :3 chance of getting it

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