A small tourist resort has a weekend traffic problem and is considering whether or not to provide emergency services to help mitigate the congestion that results from an accident or breakdown. Past records show that the probability of a breakdown or an accident on any given day of a four-day weekend is 0.25. The cost to the community caused by congestion resulting from an accident or breakdown is as follows:
• a weekend with 1 accident day costs £20,000;
• a weekend with 2 accident days costs £30,000;
• a weekend with 3 accident days costs £60,000;
• a weekend with 4 accident days costs £125,000.
As part of its contingency planning, the resort needs to know:
(a) The probability that a weekend will have no accidents
(b) The probability that a weekend will have at least two accidents
(c) The expected cost that the community will have to bear for an average weekend period
(d) Whether or not to accept a tender from a private firm for emergency services of £20,000 for each weekend during the season.