Before reading statement B, did you estimate the odds of A being true as 1?
I rolled a 100 sided die before generating statement A, and was going to claim that the first digit was 3 in A and then just put “I lied, sorry” in B if I rolled a 1. If, before reading B, you estimated the odds of A as genuinely 1 (not .99 or .999 or .9999) then you should either go claim some RSA factoring bounties, or you were dangerously miscalibrated.
I guess this is evidence that probability axioms apply to probabilities, but not necessarily to calibrated estimates of probabilities given finite computational resources- this is why in my post I was very careful to tale about calibrated estimates of P(...) and not the probabilities themselves.
Probability axioms say that P(A)>=P(A and B), not P(A)>P(A and B).
Before reading statement B, did you estimate the odds of A being true as 1?
I rolled a 100 sided die before generating statement A, and was going to claim that the first digit was 3 in A and then just put “I lied, sorry” in B if I rolled a 1. If, before reading B, you estimated the odds of A as genuinely 1 (not .99 or .999 or .9999) then you should either go claim some RSA factoring bounties, or you were dangerously miscalibrated.
I guess this is evidence that probability axioms apply to probabilities, but not necessarily to calibrated estimates of probabilities given finite computational resources- this is why in my post I was very careful to tale about calibrated estimates of P(...) and not the probabilities themselves.