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(A) The conditional probability of an event $C$ given that event $D$ has occurred is defined as $P(C|D) = \frac{P(C \cap D)}{P(D)}$.If $C \subset D$,t

Vedclass · Accepted Answer

$P(C|D) \ge P(C)$

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(A) The conditional probability of an event $C$ given that event $D$ has occurred is defined as $P(C|D) = \frac{P(C \cap D)}{P(D)}$.If $C \subset D$,then $C \cap D = C$,which implies $P(C \cap D) = P(C)$.Substituting this into the formula,we get $P(C|D) = \frac{P(C)}{P(D)}$.Since $D$ is an event,$P(D) \le 1$. Therefore,$\frac{1}{P(D)} \ge 1$.Multiplying both sides by $P(C)$,we get $\frac{P(C)}{P(D)} \ge P(C)$.Thus,$P(C|D) \ge P(C)$.

If $C$ and $D$ are two events such that $P(D) \neq 0$,then which of the following statements is correct?

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