The managers in a company are classified as top managers, middle managers, and first-line managers. Each year, 10% of top managers retire, 10% leave the company, 60% remain top managers, and 20% are demoted to middle managers. Each year, 5% of middle managers retire, 15% leave the company, 10% are promoted to top managers, 60% remain middle managers, and 10% are demoted to first-line managers. Each year, 5% of first-line managers retire, 25% leave the company, 10% are promoted to middle managers, and 60% remain first-line managers.
(a) What is the probability of a top manager eventually retiring? A middle manager? A first-line manager?
(b) If a person is currently a middle manager, what is the expected number of years that they will be with the company before either leaving or retiring?

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.4 Note: .2 7*7