# Math Help - prove or disprove complement of probability

1. ## prove or disprove complement of probability

I need to prove or disprove (E Ç F') = 1- Pr(E') - Pr(F) . I'm not deeply familiar with probability theory besides the axioms and theorems. I'd be happy with a good start or hint and can hopefully solve it from there.

Thank you!

2. Here is a counterexample.
Let $P(E)=0.4,~P(F)=0.6,~P(E\cap F)=0.2$ then it follows that $P(E\cap F')=0.2$.
But $P(E\cap F') \not=1-P(E')-P(F)=1-0.6-0.6$

3. $P(E\cap F')=0.2$
...how do you calculate that value? I'd assume Pr(F') - Pr(E) ?

4. Originally Posted by nikie1o2
$P(E\cap F')=0.2$
...how do you calculate that value? I'd assume Pr(F') - Pr(E) ?
$P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F)$

5. Ok heres another question for you! How do you know these are equal? What is the proof behind it... $P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F)$ . i know im picky but i need to document every step. thank you again

6. Originally Posted by nikie1o2
Ok heres another question for you! How do you know these are equal? What is the proof behind it... $P(E) = P(E \cap F) + P(E \cap F')\; \Rightarrow \;P(E \cap F') = P(E) - P(E \cap F)$ . i know im picky but i need to document every step. thank you again
How do I know that this is true?
Well for one, I know the basic axioms of probability.
That does not seem to be the case as far as you are concerned.
Am I mistaken there?

7. I'm just confused because if you draw a venn diagram.
$(E \cap F) + (E \cap F')$ doesnt equal E , it's equals the universe- F ?

8. You have a long way to go.
Good luck.