I think your anecdote is good. Knowing the formula for Bayes theorem isn't necessary, and I've never needed to try to do the math in my head or anything. But un

I think your anecdote is good. Knowing the formula for Bayes theorem isn't necessary, and I've never needed to try to do the math in my head or anything. But understanding probability theory, and having an intuitive feel for what probability is, is really important.