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DanielLC comments on Considering all scenarios when using Bayes' theorem. - Less Wrong Discussion
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Comments (6)
You could have improved it somewhat by using P(B|~A) instead of P(B). Doing so would make getting a higher probability than 1 impossible.
This looks like the conjunction fallacy. What you have comes out to a 6% chance that they bought you a drink and are interested, vs. a 5% chance that they bought you a drink at all.
Don't you mean 0.04?
I thought about using ~A, but estimating P(B|~A) or P(B∩~A) is also pretty difficult. There are a lot of reasons, as I've shown, why someone might by me a drink without being interested. So I still have to think about all the scenarios. Are you also saying that using the alternative form of Bayes' formula can't lead to probability > 1? (If that's the case, then that's very helpful!)
P(A and B) = P(B|A) * P(A) = 0.06
P(B) = 0.05
Yes, that's a pretty good way to see the mistake mathematically. (Dannil made the same point.)
And I've corrected the typo, thanks!
Yes. In order for you to get higher than one, P(B|~A)P(~A) would have to be negative.