- \(\quad A\) and \(B\) are two events such that
$$\mathrm { P } ( B ) = \frac { 1 } { 2 } \quad \mathrm { P } ( A \mid B ) = \frac { 2 } { 5 } \quad \mathrm { P } ( A \cup B ) = \frac { 13 } { 20 }$$
- Find \(\mathrm { P } ( A \cap B )\).
- Draw a Venn diagram to show the events \(A , B\) and all the associated probabilities.
Find
- \(\mathrm { P } ( A )\)
- \(\mathrm { P } ( B \mid A )\)
- \(\mathrm { P } \left( A ^ { \prime } \cap B \right)\)