A storm sewer network has been designed based on a $2-$ year return period storm for a $50$ year design life. What is the probability that the network will;

a$.$ Surcharge at least once in $2$ years $($the probability of failure$)?$

b$.$ Surcharge at least once during its design life?

c$.$ Flood in any one year, assuming flooding is caused by the $10-$year return period storm?

d$.$ Flood at least once in $10$ years?