2022 JPJC J2 MYE P2 Q7

Events \(A\) and \(B\) are such that \(\mathrm{P}\left( A \right)=0.5\) and \(\mathrm{P}\left( B \right)=q\), where \(0\le q < 0.5\).

1. It is given that \(P\left( A'\cap B' \right)=0.27\).
   1. Find \(\mathrm{P}\left( \left. B \right|A \right)\), leaving your answer in terms of \(q\).[3]
   2. If \(A\) and \(B\) are now known to be independent events, find \(q\).[2]
2. Find, in terms of \(q\), the range of values that \(P\left( A'\cap B' \right)\) can take.[2]