9 At a ski resort, the probability of snow on any particular day is constant and equal to \(p\). The skiing season begins on 1 November. The random variable \(X\) denotes the day of the skiing season on which the first snowfall occurs. (For example, if the first snowfall is on 5 November, then \(X = 5\).) The variance of \(X\) is \(\frac { 4 } { 9 }\).
- Show that \(4 p ^ { 2 } + 9 p - 9 = 0\) and hence find the value of \(p\).
- Find the probability that the first snowfall will be on 3 November.
- Find the probability that the first snowfall will not be before 4 November.
- Find the least integer \(N\) so that the probability of the first snowfall being on or before the \(N\) th day of November is more than 0.999 .