- Events \(A\) and \(B\) are such that
$$\mathrm { P } ( A ) = 0.5 \quad \mathrm { P } ( A \mid B ) = \frac { 2 } { 3 } \quad \mathrm { P } \left( A ^ { \prime } \cup B ^ { \prime } \right) = 0.6$$
- Find \(\mathrm { P } ( B )\)
- Find \(\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)\)
The event \(C\) has \(\mathrm { P } ( C ) = 0.15\)
The events \(A\) and \(C\) are mutually exclusive.
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.