2022 RI J2 CT Q10

For events \(A\) and \(B\), it is given that \(\mathrm{P}\left( A' \right)=0.3\) and \(\mathrm{P}\left( B \right)=0.55\).

1. Given that the events \(A\) and \(B\) are independent, find \(\mathrm{P}\left( A\cap B \right)\).[1]
2. Given that events \(A\) and \(B\) are not independent, find the range of \(\mathrm{P}\left( A\cup B \right)\).[2]
3. Given that \(\mathrm{P}\left( \left. A' \right|B \right)=0.4\), find
   1. \(\mathrm{P}\left( A\cup B \right)\),[3]
   2. \(\mathrm{P}\left( A'\cup B' \right)\).bold text[2]