Q$2.(25$p$)$ For the design flood of a spillway with an economic life of $9$ a years $($a is the last digit of your student number$)$ the accepted risk can be taken as $)($A is the last digit of your student number$)\%.$

$($a$)$ Determine the return period of its design discharge.

$($b$)$ If the cofferdam with $5$ years economic life of this large dam is designed with $20$ years flood, determine the risk of this cofferdam.

$($c$)$ Find also the probability that the design flood of the cofferdam occurs at least $3$ times in the lifetime of the spillway.

A$=5?$