# Probability

A measure that quantifies the uncertainty associated with an event.

• If an event A cannot happen, the probability p(A) is zero.
• If an event happens with certainty, p(A) is 1.
• Otherwise the values of p(A) are between zero and 1.

For a set of events, A and B, which are mutually exclusive and exhaustive, the probabilities of the individual events add up to 1. Probabilities can also be expressed as percentages, when the sum of all probabilities is 100%.

## Prior probability

The probability of an event before new evidence. Bayes's rule specifies how prior probabilities are updated in the light of new evidence.

## Posterior probability

The probability of an event after a diagnostic result, that is, the updated prior probability. It can be calculated from the prior probability using Bayes's rule.

## Conditional probability

The probability that an even A occurs given event B, usually written p(A|B). An example of a conditional probability is the probability of a positive screening mammogram given breast cancer, which is around 0.9. The probability p(A), for instance, is not a conditional probability. Conditional probabilities are notoriously misunderstood, and that in two different ways. One is to confuse the probability of A given B with the probability of A and B; the other is to confuse the probability of A given B with the probability of B given A. One can reduce this confusion by replacing conditional probabilities with natural frequencies.