Conditional probabilities

Definition

Conditional probabilities measure the likelihood of an event occurring given that another event has already occurred. They are denoted as P(A|B), meaning the probability of event A happening given that event B has happened.

5 Must Know Facts For Your Next Test

1. The formula for conditional probability is P(A|B) = P(A and B) / P(B).
2. If events A and B are independent, then P(A|B) = P(A).
3. Conditional probability can be visualized using a Venn diagram where one event is nested within another.
4. Bayes' Theorem uses conditional probabilities to update the likelihood of events based on new information.
5. The multiplication rule states that P(A and B) = P(A|B) * P(B).

Review Questions

• What is the formula for calculating conditional probability?
• How does conditional probability differ if two events are independent?
• Explain how Bayes' Theorem utilizes conditional probabilities.

Related terms

Independent Events: Two events are independent if the occurrence of one does not affect the probability of the other.

Multiplication Rule:

A rule stating that the probability of both events A and B occurring is equal to the product of their individual probabilities, adjusted for conditionality.

Bayes' Theorem: A mathematical formula used to update probabilities based on new evidence or information.