2022 ASRJC J2 MYCT P2 Q5

The events \(A\) and \(B\) are such that \(\mathrm{P}\left( A \right)=0.5\), \(\mathrm{P}\left( \left. A' \right|B \right)=0.2\) and \(\mathrm{P}\left( B\right)=0.45\). Find \(\mathrm{P}\left( \left. B \right|A' \right)\) and \(\mathrm{P}\left( A\cap B \right)\).

Determine with a reason whether events \(A\) and \(B\) are independent. It is known that event \(C\) has a probability of \(0.4\),

\(\mathrm{P}\left( A\cap B\cap C \right)=0.1\) and \(\mathrm{P}\left( B\cap C \right)=0.18\). Find the range of values of \(\mathrm{P}\left( A'\cap B'\cap C \right)\).[4]