This seems elementary, but I cannot see a quick proof:
For events $A, B, C$ we have $ P(A \mid B \cup C) \leq \max(P(A \mid B), P(A \mid C)) $
Is this right?
This seems elementary, but I cannot see a quick proof:
For events $A, B, C$ we have $ P(A \mid B \cup C) \leq \max(P(A \mid B), P(A \mid C)) $
Is this right?
It is incorrect. Consider this counter-example: $A=\{1,2\}$, $B=\{1,3\}$, $C=\{2,3\}$ and $P(\{1\})=P(\{2\})=P(\{3\})=\frac{1}{3}$.