Originally Posted by Jaywalker
...One guy insisted two engines were less reliable because you had twice the chance that one would break...
The probabilities are not causal or additive in the strictest sense.
Desert Island Fallacy
A modern airplane requires only one out of the three (or four) engines to successfully operate during flight. The chance that a well-maintained engine
fails is very small. Let the probability of engine
failure during a 14 hour flight be 0.5 percent.
P(engine failure during 14 hour flight) = 0.005 What is the probability that an airplane, powered by four engines, will safely fly from Los Angeles to Sydney Australia
? Flight time is 14 hours.
The plane will not make it to Sydney
if all four engines would fail. The probability of that happening is quite small. Using the multiplication rule
P(all four engines fail) = P(engine1 fails ∩ engine2 fails ∩ engine3 fails ∩ engine4 fails) = P(engine1 fails)•P(engine2 fails)•P(engine3 fails)•P(engine4 fails) = (0.005)4 = [5(10)-3 ]4 = 5(10)-12 = 0.000000000005
Compiled by Henry Posters
There are only five combinations of engines working/failing possible.
1. All four engines work, none fails
2. Three engines work, one fails
3. Two engines work, two fail
4. One engine works, three fail
5. All four engines fail
The sum of the probabilities of events
one to five is 1. Hence, the probability that at least one engine works is 1 – P(all four engines fail) = 1 – 5(10)-12 = 1 – 0.000000000005 = 0.999999999995 or 99.9999999995 percent.
The probability that a modern day airplane will safely complete a 14-hour flight is extremely high.