It's relatively common in embedded programming (in my experience). A lot of real-time programming is around scheduling. You certainly can use formal proofs there too, but statistical methods would be common at significant scale.

It's quite common in aerospace certification to cite systems having proven records of an acceptably-low number of failures per flight hour or similar metric.

I suspect they're using that sense of the word "proven", as opposed to a formal software proof.

Don’t know what’s going on with their certification process here but probabilistic reasoning is very common, and very reasonable, eg in cryptography.