Question

If A and B are two events such that $A⊂B$ and $P(B)≠0$,then which of the following is correct?

• A. $P(A|B)=\frac{P(A)}{P(B)}$
• B. $P(A|B)$
• C. $P(A|B)≥P(A)$
• D. None of these

Answer 1

Answer: (C)

$P(A|B)≥P(A)$

Answer 2

$A⊂B⇒A∩B=A$ and P(B)≠0⇒P(A|B)=$$\frac{P(A∩B)}{P(B)}=\frac{P(A)}{P(B)}
Since $P(B)≠0$
$∴P(A)/P(B)<1⇒P(A)$ Hence,option (C) is correct