Mathematics

Two events are independent when knowing one happened tells you nothing about the probability of the other—they don't influence each other. The key insight is that this means the probability of both occurring together equals the product of their individual probabilities: $P(A \cap B) = P(A) \cdot P(B)$. This single equation captures the idea that the events are "unrelated" in a probabilistic sense.

Two events are independent when knowing one happened tells you nothing about the probability of the other—they don't influence each other. The key insight is that this means the probability of both occurring together equals the product of their individual probabilities: $P(A \cap B) = P(A) \cdot P(B)$. This single equation captures the idea that the events are "unrelated" in a probabilistic sense.