Suppose P(A) = 0.3, P(B) = 0.4, and P(A or B) = 0.5. Find $P(A^cB)$.
Previously, I had found P(A and B) to be 0.2.
I am trying to solve the problem like so: $P(A^cB)$ = $P(A^c) + P(B) = P(A^c\,or\,B)$.
I know that $P(A^c)$ = 0.7, but how can I find $P(A^c\,or\,B)$?
One option is to go by a Venn diagram:
We are given $P(A) = a+b = 0.3$, $P(B) = b+c = 0.4$, and $P(A\mbox{ or } B) = a+b+c = 0.5$. Since the probabilities should add up to $1$, we also have the trivial observation $a+b+c+d = 1$. Convince yourself that $P(A^c B) = c$, and then find $c$ (BTW your calculation of $P(AB)$ is wrong).