- The events \(H\) and \(W\) are such that
$$\mathrm { P } ( H ) = \frac { 3 } { 8 } \quad \mathrm { P } ( H \cup W ) = \frac { 3 } { 4 }$$
Given that \(H\) and \(W\) are independent,
- show that \(\mathrm { P } ( W ) = \frac { 3 } { 5 }\)
The event \(N\) is such that
$$\mathrm { P } ( N ) = \frac { 1 } { 15 } \quad \mathrm { P } ( H \cap N ) = \mathrm { P } ( N )$$
- Find \(\mathrm { P } \left( N ^ { \prime } \mid H \right)\)
Given that \(W\) and \(N\) are mutually exclusive,
- draw a Venn diagram to represent the events \(H , W\) and \(N\) giving the exact probabilities of each region in the Venn diagram.