Given $P(E_1' \cap E_2)=a$, $P(E_2' \cap E_1)=b$, find $P(E_1)$ in terms of $a$ and $b$
Came in a test I gave today, here is what I did:
$$|P(E_1' \cap E_2) - P(E_2' \cap E_1)| =| P(E_1) - P(E_2)|$$
The above result comes from looking at the ven diagrams, I also know that:
$$ P(E_1' \cap E_2) + P(E_2'\cap E_1)=P(E_1 \cup E_2) - P(E_1 \cap E_2)$$
Again a venn diagram result, but I can't see how to move forward from here...