A highway owned and managed by a local authority is maintained by dividing it into ten segments separated at identified stations. Each segment is inspected every year and given a pavement rating of good, marginal, or poor. The degradation probability is time dependent and provided in the following table assuming no actions are in taken during the years indicated in the table to restore the pavement:

Assuming pavement conditions to be independent, what is probability of all of the pavement segments being in good condition after

(a) 1 year,

(b) 2 years,

(c) 3 years,

(d) 4 years, and

(e) 5 years.
Compute similar probabilities for the case all of the pavement segments being in marginal condition and in poor conditions. Plot the probabilities as functions of time.

Year Probability in Good Condition Probability in Marginal Condition Poor Condition Probability in First 0.99 0.01 0.00 Second 0.95 0.04 0.01 Third 0.90 0.08 0.02 Fourth 0.80 0.15 0.05 Fifth 0.60 0.30 0.10