Let A and B be two non-null events such that A B. Then, which of the following statements is always correct?

Engineering

Mathematics

Conditional Probability

Question

Let A and B be two non-null events such that A $\subset$ B. Then, which of the following statements is always correct?

P(A | B) = 1

P(A | B) $\geq$ P(A)

P(A | B) = P(B) – P(A)

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$P (A | B) = \frac{P (A \cap B)}{P (B)} = \frac{P (A)}{P (B)}$

(as A $\subset$ B ⇒ P (A $\cap$ B) = P(A))

⇒ P(A|B) $\geq$ P(A)