If events $A$ and $B$ satisfy $P(B)\neq 0$, which expression correctly defines the conditional probability of $A$ given $B$?
A$P(A/B)=\dfrac{P(A\cap B)}{P(B)}$
B$P(A/B)=\dfrac{P(A\cup B)}{P(B)}$
C$P(A/B)=\dfrac{P(A)}{P(B)}$
D$P(A/B)=P(A\cap B)\cdot P(B)$
Answer & Solution
Correct answer: A. $P(A/B)=\dfrac{P(A\cap B)}{P(B)}$
By definition, conditional probability of $A$ given $B$ is the probability that both $A$ and $B$ occur, restricted to the cases where $B$ has occurred. Hence $P(A/B)=\dfrac{P(A\cap B)}{P(B)}$.
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