Complete Independence

Complete independence in probability means that the occurrence of one event has no effect on the likelihood of another event happening. In other words, knowing that one event has occurred does not change the probability of the other event. For example, flipping a coin and rolling a die are independent events because the outcome of the coin flip doesn't influence the result of the die roll. Mathematically, the probability of both events occurring together equals the product of their individual probabilities. This concept is fundamental in understanding how certain events relate or do not relate to each other in probability theory.