Question

Which is the following statement is true?

• A. \(P(C_1 \cap C_2) \ge P(C_1) + P(C_2)\)
• B. \(P(C_1 \cup C_2) \ge P(C_1) + P(C_2)\)
• C. \(P(C_1 \cap C_2) \ge P(C_1) + P(C_2) - 1\)
• D. \(P(C_1 \cap C_2) \le P(C_1) + P(C_2) - 1\)

Hint:

Bonferroni's inequality is a direct consequence of the fact that the probability of the union of any events cannot exceed 1:
\[ P(A \cup B) \le 1 \implies P(A \cap B) \ge P(A) + P(B) - 1 \]
This is a helpful identity to memorize.

Answer 1

The Correct Option is C