According to https://en.wikipedia.org/wiki/Aviation_safety#Evolution the fatal accidents per million flights were 0.39 in 2018.

The MAX8 fleet has been operational for about six months. Assuming 3 flights per day: 350 * 6 * 30 * 3 = 0.189 million flights.

To estimate the probability of two accidents, we can use a Poisson distribution with x = 2 and μ = 0.189 * 0.39 = 0.0737

P(x=2) = e^(-μ)μ^x / x! = 0.25%

I.e your gut feeling is correct (if my math is correct, that is). If one uses the estimate from a sibling comment of 1 crash in 11 million fights, the probability decreases further to 0.01% Actually the correct calculation is:

1 - P(x=0) - P(x=1) = 0.26%

since we are looking for the probability of there being more than one plane crash -- not just the probability of there being exactly two plane crashes.

Might also be worth considering P(2 Crashes | N Miles across 350 planes where at least one operator has incompetent maintenance), because that might not be all that different from P(1 crash | N Miles across 350 planes where all operators properly maintain their planes)

Look at things like Alaska Airlines Flight 261 [0] - safe airframe, deficient maintenance, plane loses all pitch control and impacts ocean. Yes, this still means that Boeing needs to improve things - single points of failures are never OK on a plane - but it also doesn't (IMO) mean the plane is fundamentally unsafe without those fixes.

0: https://en.wikipedia.org/wiki/Alaska_Airlines_Flight_261

The mean of a Beta Distribution (2, 348) (https://www.wolframalpha.com/input/?i=beta+distribution+(2,+...) is roughly half a percent, much higher than the 1 in 11 million across all flights (https://www.quora.com/What-is-the-probability-for-an-airplan...).

(You can pretty much always make statistical inference, with uncertainty going up with the lack of data)

Depends on your assumptions, but safe aircraft will crash making the first data point meaningless as you are choosing it at the starting point. Second, you are not just running one trial on one design but many trails on many designs.

I suggest you try the math as the odds are reasonably high.

This changes if you start talking about crashes since the first commercial flight, but those are again different numbers.

>I haven’t done the math, but my gut says it would point to grounding the plane.

"Guts" are notoriously good at statistical inference

General aviation is actually quite safety focused. The entire culture is centered around safety; a large amount of private pilot training time is dedicated to the subject; human factors in particular. Go to any fly-in breakfast and talk to the pilots and inevitably at some point during the conversation you'll hear something about being a safe pilot.

That being said, the government gives general aviation pilots a fair amount of freedom once they get their license. There are rules and they are enforced; particularly when violations put the general public at risk. But there's also recognition that it's quite possible to regulate GA out of existence like a lot of other countries have, and that has pretty negative consequences in terms of pilot availability for other purposes. Therefore, regulations scale with the amount of danger the public is exposed to.

For example, ultralight aircraft (single place, <254 lbs, <=5gal fuel, <=55kts) are virtually unregulated; the idea being that they're so small and light that they aren't much danger to others. LSA/sport (1-2 place, <=1320lbs, <=120kts) are regulated; require a license and inspections but less stringent than a private license, and so on. Private licenses can't be used for commercial purposes, and generally speaking more training and endorsements or ratings are required for eg. aircraft with multiple engines; those that are >=12,500 lbs, those that land on water, those that have old-school landing gear, etc. etc.

I would liken GA enforcement to be somewhat like motorcyles. Lots of people die on motorcyles and we see bad behavior all the time, but we don't look at law enforcement and say they're doing a bad job. You're simply operating a platform with a higher probability of death than a car or truck when you do screw up.

What’s the “low altitude flying” rule that isn’t being enforced?