Question

For any two arbitrary events \( A \) and \( B \), which of the following is true?

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

Hint:

For two events, the probability of their union is less than or equal to the sum of their individual probabilities.

Answer 1

The Correct Option is C

The correct relationship is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), which satisfies the inequality \( P(A \cup B) \leq P(A) + P(B) \). The union of two events cannot exceed the sum of their individual probabilities.