I am practicing a bunch of probability problems I find through random sources and I am stuck with this one.
Suppose the probability that the engine in a single-engine fighter will fail on take-off is .005, and that the failure rate for an engine that is used in a two-engine fighter plane is 0.003. If the two-engine plane cannot take off unless both engines are operating properly, which plane is safer on takeoff?
The answer for the two-engine problem is .006 and I cannot fully grasp how they've arrived at this answer. I was thinking P(of both engines working properly)=1- P(at least one engine failing) but apparently this is not the answer.
P.S. Any problem recommendations similar to this problem will be much appreciated!
That's correct. And P(at least one engine failing) is equal to $1 - (1 - 0.003)^2 = 0.005991$, which is $0.006$ if you don't look too closely.