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Eliezer_Yudkowsky comments on Drawing Two Aces - Less Wrong
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Argument 2. Bayes' Law doesn't lie.
I'm wondering about your reasons for posting a straightforward probability question (as a top-level post rather than an Open Thread comment, no less). Are you trying to take a reading of how competent the average LW contributor currently is on trivial questions? Are you setting up a real-world problem analogous to this, where most people get the wrong answer? Or is it something else entirely?
I occasionally get requests for more homework problems. You're also correct that I was curious about the average skill level on LW.
In retrospect, though, what I should have done was start a Bayesian Fun Problems Thread. Will try to remember to do that next time I have a puzzle.