# Bayesian inference in 1760

Derivation of the Beta Distribution

The year is 1760 and Reverend Bayes observes a lottery drawn 11 times. There are a total of 10 blanks and one prize observed or a 10:1 blank:prize ratio. Intuitively the true rate is *probably* somewhere between 9:1 and 11:1. As a scholar of probability Bayes wondered how accurate this intuition is. Can *probably *be quantified as a number, what is the chance that the true rate of the lottery falls between 9:1 and 11:1? Take a moment before reading on to take a guess.