Question

Suppose for this problem that Pr[E]=19/24and Pr[F]=13/24 Pr[(E∪F)']=0 (1) What is Pr[E|F]? (2) What is Pr[F|E]?

Answer 1

use...

if Pr[(E∪F)']=0 then Pr[E∪F]=1
\[Pr[E|F]=Pr[E\cap F]/Pr[F]\]

\[1=Pr(E\cup F)=Pr(E)+Pr(F)-Pr[E\cap F]\]

Answer 2

I've never done this stuff before, but following Zarkon's tip\[Pr[E\cap F]=Pr(E)+Pr(F)-Pr[E\cup F]\]\[Pr[E|F]=\frac{Pr(E)+Pr(F)-Pr[E\cup F]}{Pr[F]}\]and extrapolating for the other one\[Pr[F|E]=\frac{Pr[E\cap F]}{Pr[E]}=\frac{Pr(E)+Pr(F)-Pr[E\cup F]}{Pr[E]}\]