2020 ACJC P2 Q5

For events \(A\) and \(B\), it is given that \(P(A\cup B)=0.8\) and \(P(\left. A \right|B)=0.5\). It is also given that events \(A\) and \(B\) are independent.

1. Find \(\mathrm{P(}B\mathrm{)}\).[2]

A third event \(C\) is such that events \(A\) and \(C\) are independent and events \(B\) and \(C\) are independent.

2. Given also that \(\mathrm{P}(C)=0.5\), find exactly the maximum and minimum possible values of \(\mathrm{P}(A\cap B\cap C)\).[3]