If A and B are two events such that A subset | vedclass

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Question

(C) Given $A \subset B$,we have $A \cap B = A$. Using the definition of conditional probability: $P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)}

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given $A \subset B$,we have $A \cap B = A$. Using the definition of conditional probability: $P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)}{P(B)}$. Since $A \subset B$,we know that $P(A) \leq P(B)$. Since $P(B) 
eq 0$,we can divide by $P(B)$ to get $\frac{P(A)}{P(B)} \leq 1$. Thus,$P(A \mid B) = \frac{P(A)}{P(B)}$. Since $P(B) \leq 1$,it follows that $\frac{P(A)}{P(B)} \geq P(A)$. Therefore,$P(A \mid B) \geq P(A)$.

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

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