4. The events \(A\) and \(B\) are such that
$$\mathrm { P } ( A ) = 0.5 , \mathrm { P } ( B ) = 0.42 \text { and } \mathrm { P } ( A \cup B ) = 0.76$$
Find
- \(\mathrm { P } ( A \cap B )\),
- \(\quad \mathrm { P } \left( A ^ { \prime } \cup B \right)\),
- \(\mathrm { P } \left( B \mid A ^ { \prime } \right)\).
- Show that events \(A\) and \(B\) are not independent.