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.