In a certain four-engine vintage aircraft, now quite unreliable, each engine has a 15% chance of failure on any flight, as
long as it is carrying its one-fourth share of the load. But if one engine fails, then the chance of failure increases to 35% for each of the other three engines. And if a second engine fails, each of the remaining two has a 45% chance of failure. Assuming that no two engines ever fail simultaneously, and that the aircraft can continue flying with as few as two operating engines, find the probability of exactly one engine failure.
Assuming that no engines fail simultaneously, the probability that exactly one engine fails is the probability that the first engine fails (15%) multiplied by the probability that the second engine does not fail (100% - 35%):
The probability of exactly one engine failure is 0.0975 or 9.75%
