# Bayes’ Theorem

Relates the probability of the occurrence of an event to the occurrence or non-occurrence of an associated event. For example, the probability of drawing an ace from a pack of cards is 0.077 (4 ÷ 52). If two cards are drawn at random, the probability of the second card being an ace depends on whether the first card is an ace or not: if it is, then the probability of the second card being an ace is 0.058 (3 ÷ 52); if not, the probability remains 0.077. Bayes’ theorem provides a mathematical rule for revising an estimate or forecast in light of experience and observation. It differs from other methods of hypothesis testing in that it assigns ‘after the fact’ (posterior) probabilities to the hypotheses instead of just accepting or rejecting them.