Probability: P(E) = P(F) = 0.7, P(F|E) = 0.9. Find....

[Paschendale]

Consider two events: E and F. P(E)=P(F)=.7
Suppose we know that P(F|E)=.9. What is the probability that at least one of them occurs?

I know that E and F are disjoint and that the answer is .77 (I have the key) but I don't know how to do it and I can't find anything in my notes to help me out.

 

[stapel]

I know that E and F are disjoint ...

How did you arrive at this conclusion?

Please be complete. Thank you!

Eliz.

 

[pka]

\(\displaystyle \begin{array}{rcl} P\left( {E \cup F} \right) & = & P(E) + P(F) - P(E \cap F) \\ & = & P(E) + P(F) - P(F|E)P(E) \\ \end{array}\)