- 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
- \(\mathrm { P } ( A \cup B )\)
- \(\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)\)
The event \(C\) has \(\mathrm { P } ( C ) = 0.20\)
The events \(A\) and \(C\) are mutually exclusive and the events \(B\) and \(C\) are independent. - Find \(\mathrm { P } ( B \cap C )\)
- Draw a Venn diagram to illustrate the events \(A , B\) and \(C\) and the probabilities for each region.
- Find \(\mathrm { P } \left( [ B \cup C ] ^ { \prime } \right)\)