Question

Addition theorem of probability is.

• A. \( P(A \cup B) = P(A) + P(B) \)
• B. \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)
• C. \( P(A \cup B) = P(A) + P(B) - P(A \cup B) \)
• D. \( P(A \cup B) = P(A) \cdot P(B) \)

Hint:

In the case of mutually exclusive events, the probability of their union is simply \( P(A \cup B) = P(A) + P(B) \), as \( P(A \cap B) = 0 \).

Answer 1

The Correct Option is B

The addition theorem of probability states that the probability of the union of two events \( A \) and \( B \) is given by: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \] This formula accounts for the fact that the overlap (intersection) of \( A \) and \( B \) is counted twice when we simply add \( P(A) \) and \( P(B) \), so we subtract \( P(A \cap B) \) to correct for that.