Question: A rapid transit system has just started operating. In the first month of operation, it was found that 25% of commuters are using the system,

A rapid transit system has just started operating. In the first month of operation, it was found that 25% of commuters are using the system, while 75% are traveling by automobile. Suppose that each month 10% of transit users go back to using their cars, while 30% of automobile users switch to the transit system.

(a) Compute the three-step transition probability p³.

(b) What will be the fractions using rapid transit in the fourth month?

(c) In the long run?

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