Probability (With a P.S. on Conspiracy Theory)

Luke Weiger lweiger at umich.edu
Thu Sep 20 20:42:22 PDT 2001



> Doesn't this depend on the question you ask. The question asked above
> (after the opening of door 1) is "What is the probability for door 2?"
> But what if you asked, instead, "What is the probability of Door 3?" and
> the answer would be
>
> prob 3 = 1-prob (door1) = 2/3.
>
> So both door 2 and door3, depending on what question you ask, have a
> probability of 2/3????
>
> Put another way, if Door 2 was red and Door 3 green, if you ask "What is
> the probability of the red door?" the answer is 2/3 red door (and hence
> 1/3 green door). But if you ask what is the probability of the green
> door, the answer is green door 2/3 (and hence 1/3 for red door).
>
> Carrol
>
> P.S. We are having fun -- but please note that confusions over
> probability are at the very heart of almost all "conspiracy theories."
> Such theories continuously assert that such and such a coincidence has a
> low probability, hence it can't be true, hence their favorite answer is
> true.
>
>
>
> Carrol

You have only a 1/3 chance of selecting the correct door unless you're endowed with prescience or in the possession of inside information. Hence, the probability that the prize is concealed behind one of the other two doors is 2/3. The host, being a rational agent, will open one of the doors (or, if you made a lucky guess, the only door) without the prize behind it. Therefore, the probability that the prize is behind one of the doors (and now, through the process of selected elimination, the only door) you didn't choose remains at 2/3. I hope that was lucid enough.

-- Luke



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