Let $P(E) = 0.4$ and $P(F) = 0.7$, with $E$ and $F$ independent. How to calculate $P(((F \cup E^c)\cap(F^c \cup E)) \mid (E^c \cap F))$?
2026-04-01 10:31:34.1775039494
problem with conditional probability and independence
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By distribution $(F\cup E^{\small\complement})\cap(F^{\small\complement}\cup E) = (F\cap E)\cup(E^{\small\complement}\cap F^{\small\complement})$
So clearly... $\mathsf P\big((F\cup E^{\small\complement})\cap(F^{\small\complement}\cup E) \;\big|\; (E^{\small\complement}\cap F)\big) \\ = \mathsf P\big((F\cap E)\cup(E^{\small\complement}\cap F^{\small\complement}) \;\big|\; (E^{\small\complement}\cap F)\big) \\ \vdots \\ = \boxed{\color{white}{0}\qquad}?$