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All I have to say about this is if you want to get an idea about how widespread ignorance and misunderstanding of basic probability theory is, just check out the
Monty Hall Dilemma. I'm constantly shocked at how few people get this one right. In fact, in one study, a majority of
math professors answered incorrectly.
And yet, it's one of the simplest applications of Bayes' Theorem out there.
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That is just gross. I read most of the "solutions"
here and I'm still shaking my head on how people can construct such elaborate yet blatantly wrong explanations.
EDIT: OK, wow,
now I'm starting to doubt myself. WTF, if switching is correct I don't know how many things I must have wrong.