3 In a large collection of coloured marbles of identical size, the proportion of green marbles is \(p\). One marble is chosen randomly, its colour is noted, and it is then replaced. This process is repeated until a green marble is chosen. The first green marble chosen is the \(X\) th marble chosen.

1. You are given that \(p = 0.3\).
   1. Find \(\mathrm { P } ( 5 \leqslant X \leqslant 10 )\).
   2. Determine the smallest value of \(n\) for which \(\mathrm { P } ( X = n ) < 0.1\).
2. You are given instead that \(\operatorname { Var } ( X ) = 42\). Determine the value of \(\mathrm { E } ( X )\).