"An Essay Towards Solving a Problem in the Doctrine of Chances" is a work on the mathematical theory of probability by Thomas Bayes, published in 1763,[1] two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price.
Contemporary reprints of the essay carry a more specific and significant title: A Method of Calculating the Exact Probability of All Conclusions Founded on Induction.
Conditionally on the value of p, the trials resulting in success or failure are independent, but unconditionally (or "marginally") they are not.
The question Bayes addressed was: what is the conditional probability distribution of p, given the numbers of successes and failures so far observed.
Bayes's preliminary results in conditional probability (especially Propositions 3, 4 and 5) imply the truth of the theorem that is named for him.
Rather, he focused on the finding the solution to a much broader inferential problem: The essay includes an example of a man trying to guess the ratio of "blanks" and "prizes" at a lottery.
He believed that Bayes's Theorem helped prove the existence of God ("the Deity") and wrote the following in his introduction to the essay: In modern terms this is an instance of the teleological argument.