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...

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, 15 P(#2 fails | #1 fails). P(#2 fails) = 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?