Brain teaser

[ving]

given the host has not opened the door that i picked there is now a 50% chance that my door has the prize...
also given that the donkey that i have decided to not go for has a bad temper there is a chance that if I dont get the prize the the donkey i get might be more friendly

I know mongo would just take the donkey and eat it.

[fillum]

Perhaps look at it this way...

On your first pick you have more likely selected a donkey (a 2 in 3 chance). So changing your selection after one of the donkey doors is eliminated by the host should improve your chances of getting the major prize. (I think? )

Perhaps the Opera users can clear it up for us ...


Cheers.

[davidd]

Look at it this way, if the host opens two doors and reveals donkeys, what do you reckon your odds are of your door having the prize?

Probably not still 1 in 3.

[Steve Axford]

But if he only opens one door, what are the odds? Still 1/3 - for your pick. But not for the remaining door, because the host has added extra information to that door - but not to your choice.

[Mary Anne]

I know mongo would just take the donkey and eat it.

Thats the only reply here that makes sense to me David

[jim]

My guess is that some of you have heard this before...

Ooh, not fair, not fair!

But maybe true. It did sound sort of familiar.

[virgal_tracy]

I saw it explained in the movie "21" with Kevin Spacey. Thinking makes my head hurt so thankfully didn't have to think this one through.

I will have to ask Mongo if Donkeys are good eating.

[ving]

its not really that hard....

you start off with a 1 in 3 chance of getting the prize, or rather lets look at it the other way... a 2 in 3 chance of getting a donkey. remove a donkey and do not get a 1 in 3 chance of a donkey as one option is removed, there are only 2 options open to kyou now... so it becomes 50% as the only options are a donkey or the prize. at this stage it doesnt matter if you change your door as the chances are the same.

i dont know how it could be otherwise or where these other theories are coming from

[lay-z]

Here it is in pictures and I hoipe you can make more sense out of it now. It doesn't become 50% because you started out with a 33.33% chance and that chance remains no matter what - you've always had three choices. The difference is you now have more information to increase your 33.33% chance of being correct. Albiet stupid, you can still pick the door that's been opened to you because that remains as an option. Unless you REALLY wanted the donkey.

[ving]

monty hall paradox... just google it
I still say the answer given is wrong.

they say picking another door changes your chance from 33% to 66% provided the host knows which door holds the prize. I find that it is irrelevant as to whether the host knows the answer or not assuming that you get what is behind the door you pick

[ving]

alan, would you care to explain how door B gets to inherit door Cs odds? there are only 2 doors left and only 2 choices, therefore a 50/50 split.

[Ms Monny]

OUCH!!

That was the sound my head just made. Still doesn't make sense.....well, it does but it doesn't!!

[ving]

50/50... take it from an opera user

[lay-z]

alan, would you care to explain how door B gets to inherit door Cs odds? there are only 2 doors left and only 2 choices, therefore a 50/50 split.

It's because this problem is about probability and not by process of elimination. The host KNOWS which door contains the prize, as s/he always opens a door with a donkey in it. What this does if give you additional information to calculate your probability of selecting the prize door.

Using "inheret" was probably a bad choice of words but what I was trying to convey is, if you stick with your original choice, you still only have 1/3 chance of winning the car. However, with the added information which of the other doors is a donkey, the remaining door has a 2/3 chance of being the prize because you are more likely to pick the donkey to begin with (2/3 chance) than the car (1/3). So basically what you've done is inverse your odds from a 1/3 probability to a 2/3 probability of winning by swapping.

Confusing, but it makes sense in my head

[Xebadir]

Lies damned lies and statistics.

Probability is a paradoxical quantity anyway, realistically the world doesn't function on two outcomes.

[Steve Axford]

Probability relies on information. Your first choice has no additional information, so your original 1/3 chance stays - no change because no new information - at least with regards that door. But - the other remaining door has new information added because the host did NOT select a door with a donkey at random. He knew where a donkey was and so he has added new information to the remaining door, but not to your original selection. Thus the two doors now have different odds. The remaining door was 1/3, but it is now 2/3 because the host selected one of the donkeys - deliberately - thus removing a 1/3 chance of selecting a donkey. Lay-z is, of course correct, but one suspects that he didn't figure this out for himself.
Another way of thinking of it is if your selection is 1/3 then the total probability must be 1 (by definition). So the remaining door must be 2/3, as 1 - 1/3=2/3. Unfortunately that way doesn't really explain why.

[ving]

ok i see where this is going... you start with a 1/3 with 3 options. one is revealed and the 1/3 remains because there was 3 options. what doesnt make sense is that your odds improve to 2/3 by changing your mind. if you change your door there are only 2 options therefore becoming 50/50 as you obviously cant pick the door already opened.

mathematically sound but incorrect as despite you mathematics the chances of winning once the first donkey is revealed is the same regardless of whether you change doors or not.

[Xebadir]

Oh and I note, even given I switched I would still pick a Donkey. Wonder why? Because no matter the probability someone always gets screwed, and I am that lucky :P.

Ever wonder why weather forecasts are wrong? Probabilistically based.

[ving]

Another way of thinking of it is if your selection is 1/3 then the total probability must be 1 (by definition). So the remaining door must be 2/3, as 1 - 1/3=2/3. Unfortunately that way doesn't really explain why.

i get that totally but still think it is wrong

[BecdS]

Holy moly brain hurt!