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To confirm the formula for probabilities, given that an event has occured, I wonder if it is true that:

$\mathbb{P}(A \mid B)=1-\mathbb{P}(A^{C} \mid B)$

where $\mathbb{P}(A)+\mathbb{P}(A^{C})=1$.

$A$ and $B$ are events.

2 Answers 2