Is $P(A|B^c) = 1-P(A|B)$? I do not think so. There are many examples in which this equality does not hold. But how do I prove it formally?
2026-04-02 03:02:53.1775098973
Prove that $P(A|B^c) \neq 1-P(A|B)$
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You cannot prove that equality never holds. For example, if $A=B^{c}$ then equality does hold. All that you can do is to give one example where equality fails.