Interesting that they mention the medical case, when there's some psychological work around the idea that we should present these cases in terms of natural frequencies instead of Bayes' theorem. The natural frequencies approach is to say "if 10000 people take the test, 100 will have cancer. Of them, 99 will get an accurate positive test, and 1 will have a false negative test. Of the other 9900, 99 will receive a fals…
It's true that when the question is formed in frequentist terms, the answer is much more intuitive. But is that how the problem occurs in real life? The doctor doesn't see ten thousand people take a test; they see a person take a test, and get either a positive or negative result. The traditional way of forming the problem seems closer to actual experience: 'your patient tested positive. you know how accurate the tes…
I suspect that this is simply a sense of scale, with the freq-vs-bayes aspect playing only a minor role.
The normalization that happens when you use percentages and 0.0 -> 1.0 probabilities is often useful, but it can sometimes obscure the magnitude of some relationships. It's easier to understand the sense of scale when you say "1 out of every 100,000 people" (which is easily extended to "a handful of people in a large city"). The same information is presented as "0.001% of the population" requires the reader to do more mental math if they want to understand how many people could be affected.
Knowing how to interpret false-positives and false-negatives is very important, but doctors are busy people who have to memorize a lot of data. It is probably better for patients if they can at least remember if something is "common" vs "rare" when they need to make a quick decision.