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Conditioning on event B restricts the sample space to only the outcomes contained within B. Within this newly restricted space, the favorable outcomes for event A are located exclusively in the intersection of A and B ($A \cap B$).

Conditions: Event B has occurred.; We are calculating the conditional probability of A given B.

Conditioning on event B restricts the sample space to only the outcomes contained within B. Within this newly restricted space, the favorable outcomes for event A are located exclusively in the intersection of A and B ($A \cap B$).

Conditions: Event B has occurred.; We are calculating the conditional probability of A given B.

For a conditioning event with positive probability, the formula is $P(A\mid B)=P(A\cap B)/P(B)$. On a Venn diagram, the overlap region ($A \cap B$) serves as the numerator, and the entire conditioning region ($B$) serves as the denominator.

Conditions: The conditioning event B has a positive probability ($P(B) > 0$).

For a conditioning event with positive probability, the formula is $P(A\mid B)=P(A\cap B)/P(B)$. On a Venn diagram, the overlap region ($A \cap B$) serves as the numerator, and the entire conditioning region ($B$) serves as the denominator.

Conditions: The conditioning event B has a positive probability ($P(B) > 0$).

Swapping the events changes both the numerator and the denominator in the conditional probability formula. $P(A\mid B)$ uses $P(A \cap B)$ as the numerator and $P(B)$ as the denominator, whereas $P(B\mid A)$ uses $P(A \cap B)$ as the numerator but $P(A)$ as the denominator.

Conditions: Events A and B have different marginal probabilities ($P(A) \neq P(B)$).; Both events have positive probability.

Swapping the events changes both the numerator and the denominator in the conditional probability formula. $P(A\mid B)$ uses $P(A \cap B)$ as the numerator and $P(B)$ as the denominator, whereas $P(B\mid A)$ uses $P(A \cap B)$ as the numerator but $P(A)$ as the denominator.

Conditions: Events A and B have different marginal probabilities ($P(A) \neq P(B)$).; Both events have positive probability.