According to most accounts of the history of Bayes’s theorem (see here and here, for example), the Rev. Thomas Bayes (1701-1761) developed his now-famous theorem in the 1740s, but he never published his work during his lifetime. Instead, it was his friend, the moral philosopher Richard Price (1723-1791), who communicated his work via a letter to physicist John Canton (1718-1772), who then read Bayes’s paper aloud to the famed Royal Society of London on Price’s behalf on 23 December 1763. (The French mathematician and astronomer Pierre-Simon Laplace (1749-1827) made additional contributions to Bayesian probability in the late 1700s; see here.)

For his part, Adam Smith’s familiarity with inverse probability is unclear at best. He was not elected a Fellow of the Royal Society until 21 May 1767, and he could not have been present at that 1763 meeting of the Royal Society in which Bayes and Price’s work on probability was discussed. Also, although Smith and Price shared mutual friends (e.g. David Hume) and moved in the same London social circles, Smith himself had a low opinion of Price. In a letter dated 22 December 1785, Smith writes: “Price’s speculations cannot fail to sink into the neglect that they have always deserved. I have always considered him as a factious citizen, a most superficial Philosopher and by no means an able calculator.” (Corr. No. 251) Ouch!

Nevertheless, although there is no other evidence that Smith engaged with or incorporated Bayesian probability theory in any of his works, the word “probably” appears a lot of times in his Wealth of Nations — by my count, 80 times in all. By way of comparison, the word “liberty” appears 88 times. (By way of further comparison, the word “probably” appears only 22 times in Smith’s Theory of Moral Sentiments, while the word “liberty” appears 15 times in TMS.) Bonus link: Check out Michael Emmett Brady’s 2013 paper, “Adam Smith’s Theory of Probability and the Roles of Risk and Uncertainty in Economic Decision Making“.