Why has Bayes' Theorem gained a central place in Statistics, what is it that was missing in the Frequentist view that Bayes' Theorem provided us?
The reason why this theorem is so important is that it allows us to update our beliefs based on the additional evidence we have. In our case, it allowed us to update our belief of having Hypoillness from 90% to a mere 0.1125%.
Another question that arises is why we overlook the additional evidence. In the context of our example, why did we overlook various factors of Hypoillness
and incline towards thinking that the probability of having the illness is 90% in the first place? Let's look at the two reasons why it happens: