The essence of my comment was that this text/test is not for me (one person of the general public) but more like a few leetcode-style questions for statisticians.
Your attempt to explain what I didn't understand just proves my point as I don't really understand what you are saying either.
And that's ok: this is just not for me! (And that's why I deleted my original comment)
> it is very important that the uncertainty in the number of trials is taken into account because over-estimating a fraction is a costly mistake.
This is not some precise jargon that is meaningless to the layman but completely clearly specified to a professional statistician. It's more like the specification written by your non-technical product manager for how some technical feature should work. A skilled data scientist will have the experience and the context to figure out what it's probably asking for, but he might write down a few more clarifying details before giving it to a junior on his team to implement.
If testing these kind of guess-what-the-stakeholder probably-means skills is the point of this test, it's quite good at it. But that's not what leetcode is for.
If "binomial distribution" and "confidence interval" are unfamiliar terms then you probably are not prepared to pass OP's "statistical reasoning test" regardless. I think most engineers wouldn't, and I only understood the intent of question 1 because my pandemic lockdown project was reading a stats textbook cover to cover.
I don’t think this is “leetcode for statisticians.” This question (and the other two) are all examples of concrete, real-world problems that people across a variety of quantitative disciplines frequently encounter.
In fact, the first question is directly relevant to voting on this site. When sorting replies by fraction of upvotes, how should the forum software rank a new reply with 1 upvote/0 downvotes, versus an older reply with 4 upvotes/1 downvote? What about an older, more controversial reply with 20 upvotes/7 downvotes? 15 upvotes/2 downvotes?
Indeed, I use this technique to sort search results in Splunk, as an extension of TF-IDF. Consider a scenario where us-east-2 is broken but us-east-1 is fine (clearly just a hypothetical!). Split the logs along that good/bad dimension, and then break down by some other pattern; log class, punct, etc. Usually I use a prior of 50:50 to help sort out the "happened once in bad cluster" events.