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

Let's draw the Venn diagram according to the question. P ( B A ) = P ( B ) P ( A ∩ B ) = P ( B ) P ( A ) This is because if A ⊂ B , then A ∩ B = A . Now, since P ( B ) ≤ 1 , we can deduce: ⇒ P ( B A ) = P ( B ) P ( A ) ≥ P ( A ) Therefore, P ( A ∣ B ) ≥ P ( A ) .

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MathematicsProbabilityConditional probabilityEasy2 minQB

MathematicsEasysingle choice

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

Options:

Answer:

Solution:

Let's draw the Venn diagram according to the question.

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

This is because if $A \subset B$ , then $A \cap B = A$ .

Now, since $P (B) \leq 1$ , we can deduce:

$\Rightarrow P (\frac{A}{B}) = \frac{P ( A )}{P ( B )} \geq P (A)$

Therefore, $P (A ∣ B) \geq P (A)$ .

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Conditional probability

⏱ 2mℹ️ Source: QB

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