Honestly I expected it to go over far more advanced topics than these, most of these are covered in the last year of high school over here.
Opening sentence: The goal of this document is to present an introduction to probability and markets in what we hope is a fairly intuitive and accessible way.
They have a whole page dedicated to that: https://www.janestreet.com/join-jane-street/interviewing/
Attention to detail and clear communication, including good grammar and spelling, are probably important.
Ask people to predict whether the Jones' have a dog and they'll start asking questions about the specifics of the Jones', like do they have children, do they live in the suburbs, have they always wanted a dog, etc. Then they try to construct a narrative based on "logical" conclusions.
When the right approach might be to ask "what's the background rate of dog ownership in the Jones' country of residence?" But that takes ignoring the specifics, and that doesn't come easily to people. It took several millennia for anyone to realise it could be useful.
This is the core idea of Bayesian statistics.
You fall back to the background rate only if you have no ability to access more pertinent facts.
The difference between Bayesian reasoning and narrative fallacy is a coherent evaluation of joint probabilities -- the bit most people skip over.
But why do you point the finger at narrative instead of a simple lack of data? In the dog example, those questions are absolutely good ones to ask, so long as the data can be found.
One reason to reject this mental opposition between 'Bayesian reasoning' and 'narrative fallacy' is because narratives are essential to coming up with good conditions on which to split the population in the first place.
'I would ask whether they have children, because children like dogs and therefore it's plausible that families with children have a higher rate of dog ownership' is a reasonable narrative that justifies collecting an extra column in your dataset.
Granted, one shouldn't accept that story uncritically without checking against the actual statistics. But narratives themselves are unavoidable even when you're doing statistics correctly!
You see this all the time in sports betting, too. People overcorrect from the base rate when receiving news. People love a narrative that makes sense to them, but statistically it rarely holds up against statistical reasoning with a very small set of variables. (For more examples, see Meehl's research around clinical vs actuarial judgment.)
Yes, you're correct that a hypothesis is one of those narratives, but if you're operating at that level of scientific abstraction you can ignore my comment. Most people don't, and just roll with the story and forget about the probabilities.
You're right that some education would help people with everyday situations. It'd be nice if schools had intro to probability and statistics as the only required math course for all students. Even just covering fractions for probabilities, mean/median/mode, and then memorizing basic tricks or terms to look up on Wikipedia/Wolfram throughout life.