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

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?

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.

To calculate the probabilities, we can use basic probability rules. Let's break down the questions one by one:

1. What is the chance that one or the other will fail?
To calculate this probability, we need to find the chance that at least one magneto fails. Since the chance of one magneto failing is 1 in 1000, the chance that it will not fail is 1 - (1/1000), which is 999/1000. Since there are two magnetos, we can assume that they are independent events. Therefore, the chance that at least one magneto fails is equal to 1 minus the chance that both magnetos work correctly. So, the probability is 1 - ((999/1000) * (999/1000)).

2. What is the chance that both will fail?
To determine this probability, we need to multiply the individual probabilities of each magneto failing. Since the chance of one magneto failing is 1 in 1000, the probability of both magnetos failing is (1/1000) * (1/1000).

3. What is the chance that neither will fail?
The probability that neither magneto fails is the complement of the probability that at least one magneto fails. So, it can be calculated as 1 - (probability of at least one magneto failing).

Please note that in real-life scenarios, these calculations may differ based on various factors, such as the nature of the system and the reliability of the components involved. It is crucial to consult appropriate references or experts for accurate calculations and assessments in practical situations.