The events $E$, $F$ and $P$ satisfy the constraints $(E \triangle F) = .7$, $P (E ∪ F) = .8$.
- (A.) Calculate $P (E ∩ F)$, making sure that is uniquely determined.
- (B.) Determine the range of possible values of $P (E)$.
- (C.) There may be independent $E,F$ events satisfying the constraints?
So I have done (A.) $P (E ∩ F) = .1$ and $P(E)+P(F)=.9$
At this point, I think that for (B.) $P(E)$ should be $<.9$ but I can't find the low limit.
For point (C.) I know that $P (E ∩ F)=P(E)P(F)$ if independent events. So I think I have to replace it on $P (E ∪ F)=P(E)+P(F)-P (E ∩ F)$ and see if the values ould exist.