I think you’re trying to decide if it’s a prank or not. And (I assume) you care about trying to come to conclusions that are likely correct. Therefore I think you should care about things that would lead you to incorrect conclusions.
Suppose the two possibilities are ‘prank made from human’s voice’ and ‘weird electromechanical phenomenon’. The logic I believe you’ve implicitly applied is that most electromechanical phenomena do not sound human and therefore this human-like sound is likely human. However I put it to you that this logic is flawed because you have not heard a randomly sampled electromechanical phenomenon but rather a sound that was sufficiently human-like to warrant an article about hauntings so thinking about the ordinary distribution of electromechanical phenomena is misleading.
Furthermore I think that you’re assigning relativity equal weight to the two possibilities of a human prankster and any kind of PA system fault when I would argue that the latter is much more common. That is, I think you’re answering a question like ‘we flipped a coin and if it came up heads, we made silly noises into a dictaphone and if it came up tails we tortured the device in some way while it was recording. We’ll play the sound and you can guess which it was’ whereas I think the answer in this case hinges a lot more on the equivalent of the coin-flipping process (eg what if you needed 10 heads in a row for the first choice? What about 15? 20?)
One can formalise this too. I’ve tried to come up with some priors that illustrate the point and which I think are reasonably generous towards your conclusion.
Say H = some human pranking a flight with silly noises,
M = some mechanical failure in the PA system,
Mh = human-sounding mechanical failure
Mm = mechanical-sounding mechanical failure
S = human-like sounds
And let’s invent some numbers for a random flight:
P(H) = 1e-6 (feels too big to me)
P(M) = 1e-3 (feels a bit small to me)
P(Mm | M) = 0.995 (I.e. 99.5% of mechanical sounds sound mechanical)
P(Mh | M) = 0.005
We read an article about S happening so we now wonder:
P(H | S). Apply Bayes theorem:
= P(H) P(S | H) / P(S)
= P(H) * 1 / P(S), and in our model
= 1e-6 / P(S).
Now what is P(S)? We can calculate in our model (assuming we’re describing all possible causes and for simplicity ignoring a flight with a human-sounding mechanical failure and a prankster).
P(S) = P(H) + P(Mh)
= P(H) + P(Mh | M) * P(M)
= 1e-6 + 0.005 * 1e-3
= 6e-6
And we can plug that back into the equation above:
P( H | S ) = 1/6
You can fiddle around with the priors and get a feel for how the affect the results but the point I want to make is that it can be true that electromechanical sounds are very rarely human-sounding and still be likely that the sounds in this case are likely electromechanical. I believe that your argument was based on the incorrect logic I described at the start of this comment and not because you had strong priors that the very unlikely event of a human prankster was more likely than the combination of the unlikely events of a faulty PA system and a fault making humanoid sounds.