Monty Hall and all that (and "painfully easy") There are two groups of people who disagree with the standard solution to the Monty Hall problem: those who know less than the person who came up with the solution and those who know more.
Steve Hutton (stevehutton at rogers dot com)
I didn't make this problem up... its a CLASSIC probability problem, and people ALWAYS try to say that the solution is wrong. You are welcome to your opinion but I must say that the solution is correct, as can be verified by asking anyone who does probability or simply doing a search on the internet for "monty hall problem".
Michael H. Pryor
So, which part of my reasoning is incorrect?
Steve Hutton
The Monty Hall problem assumes that Monty Hall doesn't care if you win or lose. If Monty Hall wants to make you lose, AND he can choose whether or not to show you the goat and offer you a trade, then it's a completely different problem.
Billy Martin
Some of the sources qualify the answer (and are thus correct); many don't (and are thus wrong). Here is a good excerpt from the sci.math FAQ:
Steve Hutton
Oops. That last note should have said "90 percent of the time when you are *right* and 10 percent of the time when you are *wrong*". The key is that the host is at least twice as likely to let a winner switch as to let a loser switch.
Steve Hutton
In stage 4, they (vehemently) make sure that whenever they pose the question, they make it absolutely clear that Monty will always open a goat door and will always offer you a chance to switch. Stage 4 people also vehemently correct anyone who mis-states the problem, and vehemently explain why it's important to state that Monty _always_ offers a chance to switch.
Adrian Gilby
An excellent analysis and an angle I hadn't considered. So let's go back to the original statement of the problem (on this website).
William Frantz
"Did Monty know what was behind the door before he showed me the goat or did he just happen to pick the goat?"
Drew Boyles
If Monty's behaviour is constrained by a rule (for example, always show a goat and offer the chance to switch), his wishes are irrelevant. If his behaviour is unconstrained, and he acts in order to increase the probability of a desired outcome, his wishes matter a lot.
Steve Hutton
Hmm. I always had problems with this as well until someone described an expansion of the problem which made it clear for me.
-ljr
Since Steve Hutton brings the actual Monte Hall into the discussion...
Jim Lyon
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