Probabilities of mutually exclusive events, given certain conditions

Question

Given $A$, $B$ and $C$ where $A$ and $B$ are mutually exclusive.

If $P(A\cap C)=0.2$, $P(B\cap C)= 0.1$, $P(C)=0.6$, $P(A\cup B)= 0.6$, $P(A\cup C)= 0.8$, and the relation $P(A) = 2P(B)$, find the probabilities of $A$ and $B$.

Answer 1

Hint: Since $A,B$ are mutually exclusive, then $P(A\cup B)=P(A)+P(B).$

Answer 2

Hint: This screams for a Venn diagram. Draw the standard one for $A,B,C$. Note that $A$ and $B$ being mutually exclusive lets you label two regions with $0$.

Answer 3

Hint : $P(A\cup C)+P(A\cap C)=P(A)+P(C)$ is true for any events $A$ and $C$.