For any events A and B, $$P ( A \mid B ) + P \left( A \mid B ^ { C } \right) = 1$$ meaning given that A occurs either B occurs or B
does not occur.

Question

Quizplus · Accepted Answer

The equation $$P ( A \mid B ) + P \left( A \mid B ^ { C } \right) = 1$$ is incorrect because it suggests that the probability of A given B and the probability of A given not B sum to 1, which is not a general rule in probability theory. The correct interpretation should involve understanding conditional probabilities separately and not assume their sum equals 1 unless under very specific conditions not described by this statement.

For Any Events a and B P(A∣B)+P(A∣BC)=1P ( A \mid B ) + P \left( A \mid B ^ { C } \right) = 1P(A∣B)+P(A∣BC)=1

For Any Events a and B $P ( A \mid B ) + P \left( A \mid B ^ { C } \right) = 1$