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brazil84 comments on The Bias You Didn't Expect - Less Wrong
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That's just not so, since the total of the two probabilities equals one. If the probability of murder with a rifle drops, the probability of murder with a handgun necessarily rises. I'm not sure how to make this point any clearer . . . . perhaps a couple equations will help:
Let's suppose that X and Y are mutually exclusive and collectively exhaustive hypotheses.
In that case, do you agree that P(X) + P(Y) = 1?
Also, do you agree that P(X|E) + P(Y|E) = 1 ?