"Thus, for statistical reasons, the more patients there are in a population, the more reliable a positive result will be. Conversely, a positive is more likely to be false in the case of rare diseases."

This description of Baye's theorem is wrong. It should say that the higher the prevalence of the disease in the population, the more reliable a positive result will be.

3blue1brown has a good yt video on the topic which I recommend:)