5.112 For simplicity, let us assume that there are two kinds of drivers. The safe drivers, which comprise 70% of the population, have a probability of 0.1 of causing an accident in a year. The rest of the population consists of accident makers, who have a probability of 0.5 of causing an accident in a year. The insurance premium is $400 times one’s probability of causing an accident in the following year. A new subscriber has an accident during the first year. What should be this driver’s insurance premium for the next year?

N = 100 p = r q = 1 - p >N lim N:q a r y

b aN - r n - y b

aN n

b

= an y

b p yqn-y p = r N : q >N