Finding the probability of an event using set theory Given: $P(A \cup B) = 0.7$, $P(A \cup B') = 0.9$, 
Find $P(A)$.
I feel like the answer has something to do with the property that 
$P(A \cup B) = P(A) + P(B) - P(AB)$ and $P(A \cup B') = P(A) + P(B') - P(AB')$, but I don't know how to get rid of $B$ and $B'$ using the properties. Thanks for any help.

Hint:  Try adding $P(A\cup B)$ and $P(A\cup B')$ and see what cancels.
Remember in particular the law of total probability: $Pr(X\cap Y)+Pr(X\cap Y') = Pr(X)$
$0.7 + 0.9 = Pr(A\cup B) + Pr(A\cup B') = Pr(A)+Pr(B)-Pr(A\cap B) + Pr(A)+Pr(B')-Pr(A\cap B')$

 $ = 2Pr(A) + \left(Pr(B)+Pr(B')\right) - \left(Pr(A\cap B) + Pr(A\cap B')\right)$

$~$

 $ = 2Pr(A) + 1 - Pr(A) = Pr(A)+1$

$~$

 so, $Pr(A) = 1.6 - 1 = 0.6$

