2024 VJC H1 Q7

The events \(A\) and \(B\) are such that \(\mathrm{P}(A \cup B) = \frac{4}{5}\) and \(\mathrm{P}(A \cap B') = \frac{1}{6}\). \(A\) and \(B\) are independent events.

1. Find \(\mathrm{P}(B)\).[2]
2. Find the probability that both \(A\) and \(B\) occur.[3]