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]?

Question

zarkon · Answer

use...

if Pr[(E∪F)']=0  then Pr[E∪F]=1
$$Pr[E|F]=Pr[E\cap F]/Pr[F]$$

$$1=Pr(E\cup F)=Pr(E)+Pr(F)-Pr[E\cap F]$$

turingtest · Answer

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$$Pr[F|E]=\frac{Pr[E\cap F]}{Pr[E]}=\frac{Pr(E)+Pr(F)-Pr[E\cup F]}{Pr[E]}$$