6 A bag contains 3 green counters, 3 blue counters and \(w\) white counters. Counters are selected at random, one at a time, with replacement, until a white counter is drawn. The total number of counters selected, including the white counter, is denoted by \(X\).

1. In the case when \(w = 2\),
   (a) write down the distribution of \(X\),
   (b) find \(P ( 3 < X \leq 7 )\).
2. In the case when \(\mathrm { E } ( X ) = 2\), determine the value of \(w\).
3. In the case when \(w = 2\) and \(X = 6\), find the probability that the first five counters drawn alternate in colour.