One of the most famous theorems in statistics and probability is that of Bayes’ Theorem, which first appeared around 250 years ago. It allows us to calculate reverse probabilities and use new evidence to update our beliefs. For example the probability of a hypothesis given a set of evidence can be found from the probability of that evidence given a hypothesis.
To understand Bayes’ Theorem it is important to have a basic understanding of conditional probability. This is the probability of something happening given that some event has already happened. Some examples of conditional probabilities are given below,
- Given that Watford scored a goal, what was the probability that Odion Ighalo scored?
- Given that it rained yesterday, what is the probability that it will remain tomorrow?
- Given a sports centre has a swimming pool, what is the probability it also has a gym?