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

Let A and B be two non-null events such that A ⊂ B. Then,… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 8 Apr · Shift I

Let

A

and

B

be two non-null events such that

A \subset B

. Then, which of the following statements is always correct.

A.
$P(A|B) = P(B) - P(A)$
B.
$P(A|B) \geq P(A)$
C.
$P(A|B) \leq P(A)$
D.
$P(A|B) = 1$

Show answer and solution

Correct option: B

Solution

Since A ⊂ B, we have P(A|B) = P(A∩B)/P(B) = P(A)/P(B). Because P(B) ≤ 1, dividing P(A) by P(B) gives P(A)/P(B) ≥ P(A). Hence P(A|B) ≥ P(A) always holds.

[JEE Main 2019 · 8 Apr · Shift I]

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