a riddle

[aGit]

Suppose i have 3 briefcases, out of which one contains 10k bush acres, and 2 absolutely nothing. Lets assume that i'd let you pick one of these briefcases, by random of course. Say you picked briefcase #1. I then open a briefcase of my choosing and show you its contents; its empty. (i know which briefcases are empty and which aint) I'd then give you one last oppotunity to switch between the briefcase you originally chose and the one that is still left.


Would you switch?



ps. long time no see, eh?

 

[Darryl]

Re: a riddle

I would, I'm more likely to get the bush acres if I swap.

I'mpretty sure we've had a very long argument about this on the forums before, but it was on the old boards, so I'll leave it open!

 

[harriergirl]

Re: a riddle

I would, I'm more likely to get the bush acres if I swap.

I'mpretty sure we've had a very long argument about this on the forums before, but it was on the old boards, so I'll leave it open!

How are you more likely?

If he takes one suitcase away then that leaves your chances at 1:2

Please explain

 

[TheNamelessWonder]

Re: a riddle

I've heard that the proper answer is that you should switch. Hell if I know why though.

 

[Bobbin]

Re: a riddle

Harrier Girl: This is why

http://en.wikipedia.org/wiki/Monty_Hall_problem

 

[Meneldil]

Re: a riddle

Indeed, essentially you have to consider each of the three possible situations.
Because the person who opens one of the briefcases knows which contains the bush acres (or which door leads to the car, etc.), and because they never choose your door, this provides extra information.
Counter intuitive, perhaps, but maths works.

 

[tomtree]

Re: a riddle

i wouldnt switch out of principle, i would stick by my first choice, i dont like indecisive people.

 

[tomtree]

Re: a riddle

now that i have read the answer, i still wouldnt switch, it says that when there are two doors left your choice still has a 1/3 chance, and the other a 2/3 chance, this is in fact a load of bullpoo, if you think about it logically, you now have two doors left each with a 1/2 chance, the one you have not chosen doesnt suddenly become more likely of having the car behind it, although i like the riddle in principle, the answer is a load of tosh.

 

[Treedude]

Re: a riddle

i wouldnt switch out of principle, i would stick by my first choice, i dont like indecisive people.

lol :winner:

 

[Darryl]

Re: a riddle

now that i have read the answer, i still wouldnt switch, it says that when there are two doors left your choice still has a 1/3 chance, and the other a 2/3 chance, this is in fact a load of bullpoo, if you think about it logically, you now have two doors left each with a 1/2 chance, the one you have not chosen doesnt suddenly become more likely of having the car behind it, although i like the riddle in principle, the answer is a load of tosh.

It's not a 50% chance though. There are three possible scenarios.

*You choose a door with the car. He opens either door, which shows a goat. If you swap, you get a goat, if you stay, you get a car.
*You choose Goat 1. He opens the door which shows Goat 2. If you swap, you get the car, if you stay, you get Goat 1
*You choose Goat 2. He opens the door which shows Goat 1. If you swap you get the car, if you stay, you get Goat 2.

So if you initially choose a goat (And the probability of you doing so is 2/3), then you will always win if you swap.

 

[tomtree]

Re: a riddle

i stick by what i said, yes, origianally there were 3 choices, but the host has effectively eliminated one of those chances by showing you the goat behind one of the doors, thus there are only two options left, your choice, or the other one, thus there is a 50% chance of the car being behind either. i will admit that if you argue it through mathmatically, then you may not have an equal, chance, but that is just rubish, and maths cant give you the answer for everything, there are often occasions where what is right mathmatically makes no sense logically (though please dont ask me for any examples as i cant think of any off the top of my head).

 

[Darryl]

Re: a riddle

As I mentioned earlier in this topic, this has come up before on the old forums, so, Tomtree, try this:

Moreover, it can easily be proven in practice.

Take three playing cards - let's say a king (car) and two two's (the goats).

Shuffle them and lay then down randomly face down. Now choose one at random.

Then check the other two cards and see if the King is there - it will be 2 times out of 3 - meaning that if you swapped you would have won two times out of three. You need to do it many times - and the more you repeat the exercise the nearer the results will be to 1/3 - 2/3 spilt.

BW - you are wrong on this one

If the card is revealed before you make your original choice it is 50/50 - but as the card is revealed after your choice then it makes no difference whatsoever to the original probability.

Or try http://math.ucsd.edu/~crypto/Monty/monty.html

 

[Bobbin]

Re: a riddle

Then tomtree, someone like me who would swap, would win on more occasions than you. Who wouldn't.

The are simple simulators around which prove that people who swap win more often than those who don't. It's simple Mathematical fact, even if it doesn't seem on the surface to make any sense.

 

[tomtree]

Re: a riddle

working it out the way you guys are may be mathmatically correct, but i believe that in practice it doesnt make any difference if you swap.

its not that i dont understand your argument, i just dont agree with it, so you will have to do something other than just re-explain it to convince me.

 

[Treedude]

Re: a riddle

working it out the way you guys are may be mathmatically correct, but i believe that in practice it doesnt make any difference if you swap.

its not that i dont understand your argument, i just dont agree with it, so you will have to do something other than just re-explain it to convince me.

read the reply that Darryl quoted from Harbi. The only way they can prove it is by carrying out many many different trials of the scenario and as Harbi said the more times you repeat it the closer the probabilities will get to being 1/3 chance you'll lose if you swap and 2/3 chance you'll win if you swap

 

[tomtree]

Re: a riddle

so your telling me if i ever get such an offer as described in the riddle, i should choose to swap?

but that goes against every moral fibre in my body!!!

im going to die priseless!!!