6 A housing estate consists of 320 houses: 120 detached and 200 semi-detached. The numbers of children living in these houses are shown in the table. A house on the estate is selected at random.
\(D\) denotes the event 'the house is detached'.
\(R\) denotes the event 'no children live in the house'.
\(S\) denotes the event 'one child lives in the house'.
\(T\) denotes the event 'two children live in the house'.
( \(D ^ { \prime }\) denotes the event 'not \(D\) '.)

1. Find:
   1. \(\mathrm { P } ( D )\);
   2. \(\quad \mathrm { P } ( D \cap R )\);
   3. \(\quad \mathrm { P } ( D \cup T )\);
   4. \(\mathrm { P } ( D \mid R )\);
   5. \(\mathrm { P } \left( R \mid D ^ { \prime } \right)\).
2. 1. Name two of the events \(D , R , S\) and \(T\) that are mutually exclusive.
   2. Determine whether the events \(D\) and \(R\) are independent. Justify your answer.
3. Define, in the context of this question, the event:
   1. \(D ^ { \prime } \cup T\);
   2. \(D \cap ( R \cup S )\).