Adam Smith’s contributions to probability theory?

In a previous post, I asked whether Adam Smith was a closet Bayesian, and I concluded that post with a reference to an obscure but intriguing paper titled “A study of Adam Smith’s original contributions to economic theory and decision making under uncertainty” by Michael Emmett Brady, a lecturer at the Dominguez Hills campus California State University. (See also his 2015 book of essays on Adam Smith and John Maynard Keynes.) Among other things, Brady’s 2016 paper identifies three passages in The Wealth of Nations as proof of “Adam Smith’s original contributions to economic theory and decision making under uncertainty.” (Brady 2016, p. 39) For reference, I reproduce the three relevant passages below: PASSAGE #1: The first passage Professor Brady cites is from Book V, Chapter 2 of The Wealth of Nations, where Smith is explaining why the business of insurance can be successfully carried out by a joint stock company in a free market, i.e. without monopoly rights: “The value of the risk,…