8 Henry makes repeated attempts to light his gas fire. He makes the modelling assumption that the probability that the fire will light on any attempt is \(\frac { 1 } { 3 }\). Let \(X\) be the number of attempts at lighting the fire, up to and including the successful attempt.

1. Name the distribution of \(X\), stating a further modelling assumption needed. In the rest of this question, you should use the distribution named in part (i).
2. Calculate
   (a) \(\mathrm { P } ( X = 4 )\),
   (b) \(\mathrm { P } ( X < 4 )\).
3. State the value of \(\mathrm { E } ( X )\).
4. Henry has to light the fire once a day, starting on March 1st. Calculate the probability that the first day on which fewer than 4 attempts are needed to light the fire is March 3rd.