The reliability of a system is defined as the probability of system fu
nctioning. In reliability theory one is studying how the reliability o
f a system can be assessed from the reliabilities of its components. I
n the first part of this paper the safety of a nuclear power plant is
considered from a reliability theory point of view. In particular, we
focus on the Chernobyl catastrophe in 1986 and the incidents at Le Bug
ey in 1984 and Barseback in 1992. Some main areas of modern reliabilit
y theory of interest for the safety of nuclear power plants are indica
ted. In the second part of the paper risk and risk aversion are consid
ered by first showing how these concepts are applied in modem non-life
insurance mathematics. At the end the link to the choice between diff
erent energy supplies is discussed.