Two events A and B are independent. Which statement correctly expresses this independence?

• A. P(A∩B) = P(A)P(B)
• B. P(A|B) = P(A)
• C. P(A∪B) = P(A) + P(B)
• D. P(B|A) = P(A)

Answer: (A)

Independence means the occurrence of one event doesn’t change the likelihood of the other. The clearest way to express this is that the probability of both events happening equals the product of their individual probabilities: P(A ∩ B) = P(A) P(B). This equality shows the joint chance of A and B is exactly what you’d expect if they don’t influence each other.

Because of this, knowing that B occurred doesn’t change the probability of A (as long as P(B) > 0), so P(A|B) = P(A). The same idea holds with roles reversed: P(B|A) = P(B). The union form, P(A ∪ B) = P(A) + P(B), would only hold if the events could not happen at the same time (mutually exclusive), which isn’t the case for independent events with positive probabilities. So the product form is the standard way to express independence.