Probability

Concept:The theorem of compound probability gives the probability of the intersection of two events using conditional probability.Explanation:For any events $A$ and $B$, the probability that both occur is $P(A \cap B) = P(A) \cdot P(B|A)$.This is the definition of conditional probability: $P(B|A) = \frac{P(A \cap B)}{P(A)}$.Among the options, only option A correctly states this: $P(A \cap B) = P(A) \times P\left(\frac{B}{A}\right)$, where $\frac{B}{A}$ denotes $B|A$.Option C is only true when $A$ and $B$ are independent, which is not stated.Options B and D involve union, not the compound probability theorem.Answer:Option A is correct.