Bayes theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one events outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes theorem formed in this way basically details how ones beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

