4

4. [Maximum mark: 7]

Events $A$ and $B$ are such that $P(A \cup B) = \frac{5}{8}$ and $P(A \cap B') = \frac{7}{24}$.

(a) Find $P(B)$. [3]

(b) Given that events $A$ and $B$ are independent, find $P(A'|B)$. [4]