Quick S2 Question

Only problem I'm having is with part c of the question but I'll post the whole question so you can see what's going on.

14) Accidents occur at a certain road junction at the average rate of 3 per year.

a) Suggest a suitable model for the number of accidents at the junction in the next month.

b) Show that, under this model, the probability of 2 or more accidents at this road junction in the next month is 0.0265 to 4 decimal places.

The local residents have applied for a crossing to be installed. The planning committee agree to monitor the situation for the next 12 months. If there is at least one month with 2 or more accidents in it they will install a crossing.

c) Find the probability that a crossing is installed.

Reply 1

Jonny W

P(January has at most one accident)
= 1 - 0.0265
= 0.9735

P(Each of the twelve months has at most one accident)
= 0.9735^12
= 0.7245

P(Crossing is installed)
= 1 - 0.7245
= 0.276