The field of Bayesian statistics is built on the work of Reverend Thomas Bayes, an 18th-century statistician, philosopher, and Presbyterian minister. His famous Bayes' theorem, which forms the theoretical underpinnings of Bayesian statistics, was published posthumously in 1763 as a solution to the problem of inverse probability. For more details on this topic, refer to http://en.wikipedia.org/wiki/Thomas_Bayes.
Inverse probability problems were all the rage in the early 18th century, and were often formulated as follows.
Suppose you play a game with a friend. There are 10 green balls and 7 red balls in bag 1 and 4 green balls and 7 red balls in bag 2. Your friend tosses a coin (without telling you the result), picks a ball from one of the bags at random, and shows it to you. The ball is red. What is the probability that the ball was drawn...