The answer is independence, which I knew, but the way it was framed around a real wallet risk scenario made me second-guess myself for a second.
Start by directly stating the core assumption: independence. Then explain what independence means in probabilistic terms and why it's necessary for the multiplication rule. Finally, connect it to practical implications in data science, especially in A/B testing and product analytics, where independence is often assumed but can be violated.
Pro tip: Mention that while independence is the key assumption, in real-world data, events are often conditionally independent given some factors; acknowledging this nuance shows depth. Also, briefly note that if events are not independent, you can use the chain rule of probability (P(A and B) = P(A) * P(B|A)) instead.
Directly answer that the events must be independent. Define independence: the occurrence of one event does not affect the probability of the other.
For independent events A and B, P(A and B) = P(A) * P(B). For more than two events, the product of their individual probabilities gives the joint probability.
If events are dependent, the multiplication rule does not hold; instead, you need conditional probabilities, e.g., P(A and B) = P(A) * P(B|A).
In A/B testing, independence is assumed between users or sessions; in product analytics, events like clicks might be assumed independent, but often they are not (e.g., user behavior). Highlight the importance of checking independence assumptions.
If independence fails, consider using models that account for correlation, such as Bayesian networks or conditional probability. Mention that independence is a simplifying assumption that may not hold in practice.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.