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I seem to be given to long-winded explanations. I've just dug around in an old University textbook of mine and came across the following passage, which maybe makes one of the key points I'm trying get across better than I can:

"Why frequencies matter
Now let us return to the question of why probability judgments - and the beliefs they express - should be influenced by relative frequencies: That is, just what is wrong with believing that a randomly selected smoker's chance of getting lung cancer is .01 when 200 out of the last 1000 smokers have gotten lung cancer? [..] The personalist's answer is that indeed it is impossible to criticize a person for any honest blieve, as long as it is consistent with his other believes. The more information there is about relative frequency, however, in general, the closer the person's belief must come to what that information says. This is a result of the requirement of coherence itself. " (emphasis mine)

I can highly recommend the book for those interested in thinking about their thinking in some depth: "Thinking and deciding" by Jonathan Baron. You do not need a mathematical background for it and it will definitely help you become better at thinking rationally and coherently.

Cheers - C.
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