If X can have the value of either 0 or 1, then is it true to say that: $$ P(Z=0|X) = P(Z=0|X=0) + P(Z=0|X=1)? $$ I tried to prove it by saying that $$P(Z=0|(X = 0 \: OR\: 1)) = \frac {P(0 \: \cap (0 \cup 1))}{P(0 \cup 1)} = \frac{P(0 \: \cap 0)}{P(0)}+\frac{P(0 \: \cap 1))}{P(1)} = P(Z=0|X=0) + P(Z=0|X=1) $$ Is my prove wrong? or the statement from the beginning is wrong?
2026-03-30 00:14:54.1774829694
Proving conditional probability statement.
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