A system consists of two identical pumps, #1 and #2. If one
pump fails, the system will still operate. However, because
of the added strain, the remaining pump is now more likely
to fail than was originally the case. That is, r 5 P(#2 fails ⏐
#1 fails)  P(#2 fails) 5 q. If at least one pump fails by the
end of the pump design life in 7% of all systems and both
pumps fail during that period in only 1%, what is the probability
that pump #1 will fail during the pump design life?

Question

A system consists of two identical pumps, #1 and #2. If one
pump fails, the system will still operate. However, because
of the added strain, the remaining pump is now more likely
to fail than was originally the case. That is, r 5 P(#2 fails ⏐
#1 fails)  P(#2 fails) 5 q. If at least one pump fails by the
end of the pump design life in 7% of all systems and both
pumps fail during that period in only 1%, what is the probability
that pump #1 will fail during the pump design life?