Chapter 10.1, Problem 28E

Insurance An insurance company classifies its drivers into three groups: G₀ (no accidents). G₁ (one accident), and G₂ (more than one accident). The probability that a G₀ driver will remain a G₀ after 1 year is 0.75, that the driver will become a G₁ is 0.20, and that the driver will become a G₂ is 0.05. A G₁ driver cannot become a G₀ (this company has a long memory). There is a 0.70 probability that a G₁ driver will remain a G_1. A G₂ driver must remain a G₂.

(a) Write a transition matrix using this information.

(b) Suppose that the company accepts 50.000 new policy holders. all of whom are G₀ drivers. Find the number in each group after the following time periods.

(i) 1 year (ii) 2 years (iii) 3 years (iv) 4 years