- The events \(A\) and \(B\) satisfy
$$\mathrm { P } ( A ) = x \quad \mathrm { P } ( B ) = y \quad \mathrm { P } ( A \cup B ) = 0.65 \quad \mathrm { P } ( B \mid A ) = 0.3$$
- Show that
$$14 x + 20 y = 13$$
The events \(B\) and \(C\) are mutually exclusive such that
$$\mathrm { P } ( B \cup C ) = 0.85 \quad \mathrm { P } ( C ) = \frac { 1 } { 2 } x + y$$
- Find a second equation in \(x\) and \(y\)
- Hence find the value of \(x\) and the value of \(y\)
- Determine whether or not \(A\) and \(B\) are statistically independent. You must show your working clearly.