TUTORIAL CHAPTER $11(40$ minutes$)$

ABC company compiled information on the reasons both new and old employees

leave the company. Some employees eventually retire, but others quit the

company prior to personal reasons, such as getting job offer. Assume that the

following matrix of one$-$year transition probabilities applies with the four states of

the Markov process being retire, leaves for personal reasons, stays as a new

employee, and stays as an old employee. Note that all old employees will retire

next year.

a$)$ Interpret the transition possibilities for the new employees.

b$)$ What percentage of the new employees will eventually retire? What percentage

will leave the company for personal reasons?

c$)$ The company currently has $1000$ employees: $800$ new employees and $200$ old

employees. How many of these employees will eventually retire? How many will

leave the company for personal reasons.