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Q.14.     If $A$ and $B$ are two events such that $A\subset B$ and $P(B)\neq 0,$ then which of the following is correct?

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

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

              (C) $P(A\mid B)\geq P(A)$

              (D) None of these

Answers (1)

best_answer

If $A\subset B$ and $P(B)\neq 0,$ then

$\Rightarrow \, \, \, (A\cap B) = A$

Also, $P(A)< P(B)$

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

We know that $P(B)\leq 1$

$1\leq \frac{1}{P(B)}$

$P(A)\leq \frac{P(A)}{P(B)}$

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

Hence, we can see option C is correct.

Posted by

seema garhwal

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