Math Help - Probability

1. Probability

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 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. Thanks.

2. Hello, Paschendale!

Consider two events: $E\text{ and }F$, where $P(E)\:=\:P(F)\:=\:0.7$

Suppose we know that: $P(F|E)\:=\:0.9$

What is the probability that at least one of them occurs?

Your notes must include Bayes' Theorem: . $P(F|E) \;=\;\frac{P(F \cap E)}{P(E)}$

So we have: . $P(F|E) \;=\;\frac{P(F \cap E)}{0.7} \;=\;0.9 \quad\Rightarrow\quad P(F \cap E) \;=\;0.63$

Then: . $P(F \cup E) \;=\;P(F) + P(E) - P(F \cap E)$

. . . . . . . . . . . . $= \;\;\;0.7 \;\;+\;\; 0.7 \;\;-\;\; 0.63$

. . . . . . . . . . . . $=\;\;\;0.77$

3. Ok I think I get it. Thanks dude.