I have an airplane that has an ignition system that works like this. There are 2 energy producing devices, called magnetos

Question

that "fire" the spark plugs, 2 per cylinder. There is a 1 in a 1000 chance that one will fail.
What is the chance that one or the other will fail?
What is the chance that both will fail?
What is the chance that neither will fail?

Answer 1

probability one will fail : 1/1000 * 999/1000 * 2

prob both will fail: 1/1000 ^2

Prob neither: (999/1000)^2

check: all three of these should add to 1.

999*2/1E6+ 1/1E6 + 999^2/1E6

999(2+999) + 1 / 1E6=

(1000-1)(1000+1)+ 1 /1E6
1E6-1+1 /1E6 = 1 checks.