The question:
Once a year employees at a company are given the opportunity to join one of three pension plans, A, B or C. Once an employee decides to join a plan they cannot drop out or switch. Past records indicate that each year 4% elect to join pension A, 14% elect to join pension B and 7% join pension C. The remainder do not join any plans.
A) In the long run, what percentage of the employees will elect to join plan A, B, and C?
B) On the averag, how many years will it take an employee to decide to join a plan?
My problem with the question:
I am having troubles applying the formula (I-Q)^-1 because when i do I-Q i get a matrix that has zeros at the top and has no inverse. Please show me how to get past this issue. Thanks