Conditional probability

Conditional probability is a concept in probability theory that calculates the probability of an event given the occurrence of another event. It is a fundamental concept in statistics and data analysis, and is used in a variety of fields, including medicine, psychology, and economics.

Definition

In probability theory, the conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This is usually expressed as P(B|A), which reads as "the probability of B given A".

Calculation

The calculation of conditional probability is based on the formula:

P(B|A) = P(A ∩ B) / P(A)

where:

• P(A ∩ B) is the probability of both events A and B occurring
• P(A) is the probability of event A occurring

Applications

Conditional probability has a wide range of applications in various fields. In medicine, it is used in epidemiology to determine the likelihood of a disease given a certain condition or exposure. In psychology, it is used in behavioral studies to predict behavior based on past actions. In economics, it is used in risk assessment and decision making.

See also

• Probability theory
• Bayes' theorem
• Joint probability
• Independent events
• Dependent events

References

• Conditional probability
  Conditional probability
• Probability tree diagram
  Probability tree diagram
• Venn Pie Chart describing Bayes' law
  Venn Pie Chart describing Bayes' law
• Bayes theorem visualisation
  Bayes theorem visualisation