Conditional Probability Definition

Probability · Axiom Academy

LESSON Conditional Probability Definition Understanding how probability changes when given additional information 1. The Concept of Conditional Probability When we know that event B has occurred, it changes the sample space and affects the probability of event A. We denote this as P(A|B), read as "the probability of A given B." 2. Visualizing with Venn Diagrams When B occurs, our sample space reduces to just B. The conditional probability P(A|B) is the portion of B that overlaps with A, relative to all of B. Since we know B has occurred, we rescale probabilities so that P(B) becomes our new "whole." The intersection A∩B represents outcomes where both A and B occur. 4. The Conditional Probability Formula This formula is valid whenever P(B) > 0. If P(B) = 0, then conditional probability is undefined, as we cannot condition on an impossible event.

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