Monty Hall Problem

[Ghost Post]

Murray and others have mentioned that those who answer 1 / 2 to the Sleeping Beauty Paradox would also probably answer 1 / 2 to the probability of getting the desired object in the Monty Hall Problem. Are there any further thoughts?

Are there any of you who maintain that it is not better to switch? If so, I would appreciate your reasoning. I think that this question is very relevant to the Sleeping Beauty Paradox.


[This message has been edited by Derkage (edited 06-21-2000).]

[dethwing]

I say 1/2 on SB and 2/3 on Monty Hall. So your reasoning is not true in my case.
As to my reasoning on the SB case, heads is heads and tails is tails no matter what day it is, when its asked, or whether the guy is wearing a plaid shirt, talking in french or any other spin you want to put on it. Peace
"I wish I had a motto.....Thats it!!!! 'I wish I had a Motto' "

[extropalopakettle]

Monty Hall - switch. No debate.
SB - 1/2 probability heads. Much debate.

Monty Hall was never considered a paradox, just slightly counterintuitive before a little analysis is done.

The problem with this SB puzzle is that the arguments for 1/3 seem reasonably valid until you consider the implications (see my post "1/2 before, 1/3 during, 1/2 after" in the "other forum"). The implications are what make this a paradox, and my opinion about paradoxes is that they don't really exist, i.e. they exist in our minds as long as we fail to reason correctly. Sound logic does not derive contradictions from true premises. If you derive a contradiction, don't stop and say "ooh, a paradox" - find the fault in the logic or the false premise.

No contradictions arise from Monty Hall.

I will say, though, that many who are saying 1/2 (not I, of course!) are doing worse math than most of those who are saying 1/3. But bad math doesn't win over worse math (answer-wise) when the worse math coincidentally produces the same answer as correct math. I just haven't yet found the correct math. But the contradictions that arise from the 1/3 answer mean it must be wrong.

The "no right answer" answer is even starting to sound appealing to me.

There is a subtle distinction (I hope!) between "the probability the toss was heads" and "the probability that this question/situation/awakening, of the three possible ones, is the single one that occurs in a situation where the toss was heads". I think we've all just failed to formalize the latter properly.

[Ghost Post]

I'm really confused again, you may say I am doing bad math, but it sounds like you guys ae assuming way to much. With the Monty Hall Problem, it doesn't matter whether your first guess is right or wrong, you are still shown a chocolate bunny behind another door. You know that there are two doors left, and you know that one door is hiding a gold bunny and one is hiding a chocolate bunny. So there is now a one in two chance that the first door you picked is right, and a one in two chance that the first door you picked is wrong. What am I doing wrong?
And with the Sleeping Beauty problem, it's the same thing. No matter what has happened, no matter what day it is, no matter where you were yesterday, if you flip a coin, the chances of it being heads is one in two. Always.
Can someone please write me back and end this nagging disequilibrium that you have all created for me? Tell me, in English, without assuming anything, what is wrong with my basic logic, or tell me why these problems do not have an answer, or even better, tell me why I am absolutely right. And Soon!!

Crackristen420@hotmail.com

[worm]

kristen, have you read through this thread about the problem. if you haven't i think it's explained over and over in understandable terms.

[worm]

oops, i think i cut off the l on my html. i'll try that again. This thread

[HyToFry]

worm, what is your stand on this, i'm leaning both ways, 50/50 makes sense, but if the coin comes up heads, there will be another 50/50 chance.

the way i see it there are three possibilities.

1. Coin Comes up Tails, 50% of the time
2. Coin comes up Heads, then Tails 25% of the time.
3. Coin Comes up Heads, then Heads 25% of the time.

This puts the odds on the first day of 50% heads and 50% tails, same for the second day, but when you put them together, that doesn't change those odds... does it?

[worm]

here's what i think, for what it's worth...

sleeping beauty:

it is obviously 1 in 2 for the original toss.

a subsequent toss, as a result of getting a heads on the first toss, is a separate event in my opinion and is still a 1 in 2 deal.

so, if i were in sleeping beauty's place, i would answer "1 in 2" because i would want to get the answer right.

monty hall:

if you pick the wrong door at the start, a 2 in 3 chance, he has to reveal the one remaining bad door. so switching gives you the right door.

if you pick the right door, a 1 in 3 chance, he can reveal either of the remaining doors. switching in this case equals losing.

switching will double your chances of winning.

how they differ:

with sleeping beauty the result of the first event (a coin toss) doesn't affect the result of the second event (another coin toss); it only determines whether there will be a second event. with monty hall the result of the first event (your pick) does affect the result of the second event (monty's pick).

well that's what i think. does it make sense to everyone or anyone?