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 = P(#2 fails | #1 fails)
> P(#2 fails) = q. If at least
one pump fails by the end of the pump design life
in 13% of all systems and both pumps fail during that
period in only 3%, what is the probability that pump #1 will
fail during the pump design life?