Actually being able to do stuff with Bayes law by hand is going to be not only hard to teach, but probably impossible to remember for those of us who don't actually do math in real life. People forget stuff after a few months or years.
I highly doubt the average person is interested in checking the math on a science paper, so if you want the general public to understand statistics you... have to show us all a reason to, and also teach us all of the related skills needed to make it useful. Or else.... we will all just forget, even with the best teacher in the world.
Most of us aren't doing random game engines as a hobby project or testing things on bacteria cultures.
Maybe they should teach it in context of how to understand a scientific paper, since that's one of the more relevant things for non-pros. If you just teach statistics alone people will say
"Ok, now I know that it's easy to lie to yourself if you don't use any numbers but I don't have collections of large numbers of data points in my life to actually analyze"
If you have a way to fix this, you would be set for life, going around playing a sort of corduroy jacketed Robin Hood, keeping the rich from stealing from the poor.
Realistically, it is (somewhat) fixable in small contexts. I've worked (and continue to work) on teams that are somewhat decent at risks and probabilities, but it's definitely an exceptional experience.
I don't know how to widely teach that. But I'm not yet ready to give up and say "it can't be taught", because those folks on my team are the counterexamples.
That’s a pretty good bar and I wonder if we could just cut to that chase earlier. But I also believe that people need enough math to see when they’re being cheated, and I feel like you could just tell middle schoolers that and they would pay attention. Maybe even primary school.
You told Billy he could have three apples, and now there are two left. Did Billy take more apples than he should have?
It’s always how do you share your cookies fairly with your friends and if they’re my cookies why do I have to share them at all? Screw “fairly” I’m keeping the extras at least. That sort of sharing is a socially advanced concept they don’t entirely get just yet.