Is it possible to calculate the conditional probability conditioning on the complement given we know the probability conditioning on the event itself?
2026-04-10 08:25:27.1775809527
Is it possible to calculate $P(X | Y)$ from $P(X | \neg Y)$?
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In general, two events have three independent associated probabilities from which the others can be calculated. These can be expressed in different "bases", for instance $\{ P(X),P(Y),P(X \cup Y) \}$ and $\{ P(X),P(Y),P(X \cap Y) \}$. Of course conditionals can also be in these "bases".
Giving just one of these is not enough to obtain all the others. Actually, just specifying one of these doesn't tell you anything about the other, it could be anywhere between zero and one inclusive.
More generally $n$ events have $2^n-1$ associated probabilities to specify: there are really $2^n$ measures to specify but the normalization condition specifies one of them by default.