How do I find the probability of these independent events The following is taken from the ETS math review for the GRE:

Let A, B, C, and D be events for which P(A or B)=0.6, P(A)=0.2, P(C or D)=0.6, and P(C)=0.5 The events A and B are mutually exclusive, and the events C and D are independent. 
Find P(D).

I'd appreciate it if someone could show me how to solve this. The answer is given as 0.2, but I don't know how it's arrived at. Thanks!
Using the independence of $C$ and $D$ we have that
$$
P(C)P(D)=P(C\cap D)=P(C)+P(D)-P(C\cup D).
$$
Use this to find $P(D)$. You don't need to involve $A$ and $B$ to find $P(D)$.
P(c∩d)= 0 as they are independent so

p (c∪d)= p(c)+p(d)-P(c∩d)

so p(d)= 0.6-0.5

p(d)=0.1