Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).