Conditional probability

How it is used

Calculated as P(A and B) / P(B). Central to medical testing, risk analysis and Bayes' theorem. A classic mistake is to treat P(A | B) and P(B | A) as the same, for example confusing the chance of a positive test given disease with the chance of disease given a positive test.

Example sentences

1. What is the conditional probability that a customer buys again, given that they complained last month?

2. The table lets you read off conditional probabilities for each age group.

Common collocations

• conditional probability of A given B
• calculate a conditional probability
• conditional on
• given that

Related terms

• probabilityA number between 0 and 1 that expresses how likely an event is: 0 means it cannot happen and 1 means it is certain.
• Bayes' theoremA rule for updating the probability of an event or hypothesis in the light of new evidence, linking P(A | B) to P(B | A): P(A | B) = P(B | A) × P(A) / P(B).
• independent eventsEvents where knowing that one has happened does not change the probability of the other; for two such events, P(A and B) = P(A) × P(B).
• cross-tabulationA table that shows how the categories of two or more categorical variables combine, with the number of cases in each combination.

More terms: Probability

• random variable
• expected value
• mutually exclusive