Chapter 9.1, Problem 94E

Dental insurance. Refer to Problem 93. During the open enrollment period, university employees can switch between two available dental care programs: the low-option plan (LOP) and the high-option plan (HOP). Prior to the last open enrollment period, $40\%$ of employees were enrolled in the LOP and $60\%$ in the HOP. During the open enrollment program, $30\%$ of employees in the LOP switched to the HOP and $10\%$ of employees in the HOP switched to the LOP.

(A) Write the transition matrix.

(B) What percentage of employees were enrolled in each dental plan after the last open enrollment period?

(C) If this trend continues, what percentage of employees will be enrolled in each dental plan after the next open enrollment period?