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#1 Re: Guestbook » Flaws in logic of solution to a couple of the logic problems » 2014-01-21 20:44:12

ILIA wrote:

Let's say I originally picked door 1 then door 2 was opened showing the goat so we want to calculate probability of car behind door 1 given that door 2 has a goat and probability of car behind door 3 given that door 2 has a goat.

The flaw in your problem definition is the condition  "given that door 2 has a goat", it should be "given Monty opens Door 2"
.
If we call the 'probability that Monty opens Door 2', p(g2), then:
p(g2) = (1/3*1)  + (1/3 * 1/2)  + (1/3 * 0) = 1/2 and
p(g2)|(c1) = 1/2 and p(g2)|(c3) = 1

Plug those values into Bayes and you get 1/3 and 2/3

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