Question:
Let A and B be two non-null events such that \(A \subset B\). Then, which of the following statements is always correct?
Let A and B be two non-null events such that \(A \subset B\). Then, which of the following statements is always correct?
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If \(A \subset B\) then \(A \cap B = A\), so \(P(A|B) = \frac{P(A)}{P(B)}\) and \(0 \lt P(B) \le 1\).
Updated On: Nov 5, 2026
- \(P(A|B) = 1\)
- \(P(A|B) = P(B) - P(A)\)
- \(P(A|B) \le P(A)\)
- \(P(A|B) \ge P(A)\)
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The Correct Option is D
Solution and Explanation
Since \(A \subset B\), \(A \cap B = A\), hence \(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)}{P(B)}\).
As B is non-null, \(0 \lt P(B) \le 1\), so \(\frac{1}{P(B)} \ge 1\) and \(P(A|B) \ge P(A)\).
Option (1) holds only if \(P(A) = P(B)\), not always; option (2) is generally false; option (3) fails when \(P(B) \lt 1\) and \(P(A) \gt 0\).
Answer: (4) \(P(A|B) \ge P(A)\)
As B is non-null, \(0 \lt P(B) \le 1\), so \(\frac{1}{P(B)} \ge 1\) and \(P(A|B) \ge P(A)\).
Option (1) holds only if \(P(A) = P(B)\), not always; option (2) is generally false; option (3) fails when \(P(B) \lt 1\) and \(P(A) \gt 0\).
Answer: (4) \(P(A|B) \ge P(A)\)
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