3. Accidents occur randomly at a road junction at a rate of 18 every year.
The random variable \(X\) represents the number of accidents at this road junction in the next 6 months.
- Write down the distribution of \(X\).
- Find \(\mathrm { P } ( X > 7 )\).
- Show that the probability of at least one accident in a randomly selected month is 0.777 (correct to 3 decimal places).
- Find the probability that there is at least one accident in exactly 4 of the next 6 months.