This is my first post so you may want to check it with someone who knows something about this
Anyway I googled the problem and it came up with this
P(A or B) = .60 and P(A) =.20 ... How do I find P(B) given that A and B are independent? - Yahoo! Answers
The trouble is that it gives more than one answer .5 and .4 are both suggested. Personally I find .5 more convincing. Anyway below is the best argument I found on the link.
There's a 40% chance of not A or B
There's an 80% chance of not A
Thus there's a 40% chance of B but not A
Now, given not A, there's a 50% chance of B (40%/80%)
Since A and B are independent, there must be a 50% chance of B regardless of the condition of A.