Independent events with an unknown probability, the probability of both and why the events are not mutually exclusive

The events \(A\) and \(B\) are independent, with \(P(A)=0.6\) and \(P(B)=x\).

1. Write down, in terms of \(x\), an expression for \(P(A\cap B)\).[1]
2. It is also given that \(P(A\cup B)=0.8\).[4]
   1. Find \(x\).
   2. Find \(P(A\cap B)\).
3. Hence explain why \(A\) and \(B\) cannot be mutually exclusive.[1]