Bayes Theorem by Andy Hayes

Applications of the theorem are widespread and not limited to the financial realm. As an example, Bayes' theorem can be used to determine the accuracy of medical test results by taking into consideration how likely any given person is to have a disease and the general accuracy of the test.

Bayes' theorem gives the probability of an event based on information that is or may be related to that event. The formula can be used to see how the probability of an event occurring is affected by new information, supposing the new information is true. For example, say a single card is drawn from a complete deck of 52 cards. The probability the card is a king is four divided by 52, or approximately 7.69%, since there are four kings in the deck. Now, suppose it is revealed the selected card is a face card. The probability the selected card is a king, given it is a face card, is four divided by 12, or approximately 33.3%, since there are 12 face cards in a deck.