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Solution to Monty Hall Problem
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The key to my understanding of this problem is to assume that Monty
Hall has no choice. He must always respond by showing you a
door with
a goat.
You had a two-thirds chance at the start to pick the
losing door. In this case, Monty must show you the only other
losing
door. So two-thirds of the time, when he shows you the door
with the
goat, the other door will have the automobile. Therefore, you
have a
two-thirds chance of winning by switching.
The problem gets more
complex if we assume an "evil Monty" or an "angel Monty" who
preferentially chooses whether to show a door with the goat depending
on whether your initial choice was good or bad, and whether he prefers
that you win or that you lose. There could also be a "random
Monty"
who flips a coin to decide whether or not to show a door with a
goat.
Your odds would also be affected depending on whether or not you knew,
or suspected, that Monty was evil, good or random.
I haven't
done a detailed analysis of these more complex scenarios, but my
initial analysis is that some of them would change the odds.
The
chances of winning by switching would no longer be two-thirds in some
of these scenarios. My solution is limited to the case where
Monty has
no choice. You'll need to analyze further yourself, or read
the
analyses of others, if you want to address these more complex scenarios.
I
intentionally avoided researching the problem on the web. I
wanted to
solve it myself. I've since done a Google search and found
much information on this and related problems. For your
convenience, I've also included some Google links on this page..
Herman Held
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