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The derivation of Bayes' theorem requires that the conditioning probabilities be nonzero. Specifically, when deriving $P(A|B)$ from the intersection, we divide by $P(B)$, so $P(B)$ must be positive.

Conditions: Deriving Bayes' formula from conditional probability definitions.; $P(B) > 0$ for $P(A|B)$ to be defined.; $P(A) > 0$ for $P(B|A)$ to be defined.

The derivation of Bayes' theorem requires that the conditioning probabilities be nonzero. Specifically, when deriving $P(A|B)$ from the intersection, we divide by $P(B)$, so $P(B)$ must be positive.

Conditions: Deriving Bayes' formula from conditional probability definitions.; $P(B) > 0$ for $P(A|B)$ to be defined.; $P(A) > 0$ for $P(B|A)$ to be defined.

In the square diagrams, the braces represent proportions of areas. $P(A)$ is the fraction of the total sample space where event A occurs (a vertical strip).

Conditions: The visualization assumes probabilities can be represented by relative areas.; Both A and B have positive probability for the ordinary conditionals used here.

In the square diagrams, the braces represent proportions of areas. $P(A)$ is the fraction of the total sample space where event A occurs (a vertical strip).

Conditions: The visualization assumes probabilities can be represented by relative areas.; Both A and B have positive probability for the ordinary conditionals used here.