Decision Making with Risk$-$ Exercise

An engineer is to choose between Design A and Design B for the construction of a civil engineering system. The longevity of the system with Design $\backslash ($ A $\backslash )$ in the absence of climate change is $35$ years$($which occurs $4$ out of every $10$ times$),$ whereas the longevity of the system with Design $\backslash ($ A $\backslash )$ in the presence of climate change $($which occurs $6$ out of every $10$ times$)$ is $25$ years.

The longevity of the system with Design B in the absence of climate change is $20$ years $($which occurs $8$ out of every $10$ times$),$ whereas the longevity of the system with Design B in the presence of climate change $($which occurs $2$ out of every $10$ times$)$ is $15$ years.

The probabilities of occurrence of presence of climate change and absence of climate change is unknown.

State what kind of decision making is involved in this case.

a$.$ Risk b$.$ Uncertainty

List the following:

$1.$ Actions

$2.$ States of nature

$3.$ Payoffs

Choose the best suited alternative using Decision Tree.