Theoretically lets suppose under a certain assumption that an event 'e' has the probability of being labelled 'A' as a function of time t by a monotonically increasing function,
(1) p(e==A,t) = 1 - (1/2)^t
of course,
(2) p(e==!A,t) = 1 - p(e==A,t)
where '!A' is not A. Now if I conduct an experiment and I find that 'e' != 'A' (i.e. 'e' is not equal to 'A') by some value of t, where p(e==A,t) is very large, then what can I say about the p(e==NA,t) numerically?
As an example, at t=10, p(e==A,10)=0.99805 and if I find that at t=10, that 'e' != 'A'. What can I say about p(e==!A,t).
It seems to me that since by that time with such a huge probability of 'e' = 'A' occurring, but in reality not occurring, then this should imply that
'e' != 'A' with high probability. But this contradicts (2), where p(e==!A,10) = 0.00195!
Is this logic in incorrect? Am I overlooking something?
Thanks for any insight into the matter.
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