Question

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.

Answer 1

Answer:

0.0975 or 9.75%

Step-by-step explanation:

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%):

$P = 0.15*(1-0.35)\\P=0.0975$

The probability of exactly one engine failure is 0.0975 or 9.75%