Q

# Need explanation for: - Statistics and Probability - JEE Main-3

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

• Option 1)

$P(A\mid B)\leq P(A)$

• Option 2)

$P(A\mid B)\geqslant P(A)$

• Option 3)

$P(A\mid B)=1$

• Option 4)

$P(A\mid B)=P(B)-P(A)$

Views

$A$ and $B$ non null events (given)

$A\subset B$

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

Since $P(B)\leq 1$

$\Rightarrow \frac{P(A)}{P(B)}\geqslant P(A)$

Option 1)

$P(A\mid B)\leq P(A)$

Option 2)

$P(A\mid B)\geqslant P(A)$

Option 3)

$P(A\mid B)=1$

Option 4)

$P(A\mid B)=P(B)-P(A)$

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