1. 1. In the Venn diagram below, \(A\) and \(B\) represent events and \(p , q , r\) and \(s\) are probabilities.
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$$\mathrm { P } ( A ) = \frac { 7 } { 25 } \quad \mathrm { P } ( B ) = \frac { 1 } { 5 } \quad \mathrm { P } \left[ \left( A \cap B ^ { \prime } \right) \cup \left( A ^ { \prime } \cap B \right) \right] = \frac { 8 } { 25 }$$

1. Use algebra to show that \(2 p + 2 q + 2 r = \frac { 4 } { 5 }\)
2. Find the value of \(p\), the value of \(q\), the value of \(r\) and the value of \(s\)
   (ii) Two events, \(C\) and \(D\), are such that $$\mathrm { P } ( C ) = \frac { x } { x + 5 } \quad \mathrm { P } ( D ) = \frac { 5 } { x }$$ where \(x\) is a positive constant.
   By considering \(\mathrm { P } ( C ) + \mathrm { P } ( D )\) show that \(C\) and \(D\) cannot be mutually exclusive.