If events A and B are independent, P(A ∩ B) equals what?

• A. P(A)P(B)
• B. P(B|A)
• C. P(A) + P(B)
• D. min(P(A), P(B))

Answer: (A)

Independence means the occurrence of one event doesn’t change the likelihood of the other. So the chance that both A and B happen is the product of their individual chances: P(A ∩ B) = P(A)P(B). That’s why the product is the correct expression for the intersection when A and B are independent. The other forms don’t describe the joint probability: P(B|A) is the probability of B given A (which equals P(B) when independent, not P(A)P(B) unless P(A)=1); P(A) + P(B) adds the chances and is not the intersection; min(P(A), P(B)) is just a bound, not a joint probability.