$2.$ The $40-$year design discharge is used in a drainage system. It is expected that after $15$ years, the drainage system will be replaced by a new drainage structure $($service life $\backslash (=\backslash )15$ years$)$

a$)$ What is the probability that the design discharge will be exceeded on the first $2$ years after construction?

b$)$ What is the probability that the design discharge will be exceeded two times over the period of $15$ years?

c$)$ Compute the risk and reliability of the project throughout its service life.

d$)$ If the return period is $50$ years, what is the probability that the design discharge will not be exceeded exactly on $5$th and $10$th year for a period of $15$ years?