3. The probability that Ajita gets up before 6.30 am in the morning is 0.7 The probability that she goes for a run in the morning is 0.35
The probability that Ajita gets up after 6.30 am and does not go for a run is 0.22
Let \(A\) represent the event that Ajita gets up before 6.30 am and \(B\) represent the event that she goes for a run in the morning. Find

1. \(\mathrm { P } ( A \cup B )\),
2. \(\mathrm { P } \left( A \cap B ^ { \prime } \right)\),
3. \(\mathrm { P } ( B \mid A )\).
4. State, with a reason, whether or not events \(A\) and \(B\) are independent.