- Given that
$$\mathrm { P } ( A ) = 0.35 \quad \mathrm { P } ( B ) = 0.45 \quad \text { and } \quad \mathrm { P } ( A \cap B ) = 0.13$$
find
- \(\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)\)
- Explain why the events \(A\) and \(B\) are not independent.
The event \(C\) has \(\mathrm { P } ( C ) = 0.20\)
The events \(A\) and \(C\) are mutually exclusive and the events \(B\) and \(C\) are statistically independent. - Draw a Venn diagram to illustrate the events \(A , B\) and \(C\), giving the probabilities for each region.
- Find \(\mathrm { P } \left( [ B \cup C ] ^ { \prime } \right)\)