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

Question

Quizplus · Accepted Answer

This is because $P(A|B)$ represents the probability of A given B, and $P(A^C|B)$ represents the probability of not A (the complement of A) given B. Since either A or not A will occur, their probabilities sum to 1.

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

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