- (a) State in words the relationship between two events \(R\) and \(S\) when \(\mathrm { P } ( R \cap S ) = 0\)
The events \(A\) and \(B\) are independent with \(\mathrm { P } ( A ) = \frac { 1 } { 4 }\) and \(\mathrm { P } ( A \cup B ) = \frac { 2 } { 3 }\) Find
(b) \(\mathrm { P } ( B )\)
(c) \(\mathrm { P } \left( A ^ { \prime } \cap B \right)\)
(d) \(\mathrm { P } \left( B ^ { \prime } \mid A \right)\)