In a probability experiment, what does it mean if an event is independent?

In probability theory, independence between events signifies that the occurrence of one event does not influence the probability of the other event occurring. This means that if two events are independent, knowing that one event has happened provides no information about whether the other event will happen or not.

For instance, if event A is the event of rolling a die and event B is the event of flipping a coin, the outcome of the die roll does not affect or change the outcome of the coin flip. Each event operates completely independently of the other, allowing their probabilities to multiply directly when calculating the probabilities of both events occurring together.

Independence is a fundamental concept in probability that helps in understanding how different scenarios interact. This helps in calculating overall probabilities in complex situations involving several independent events, where the total probability can be simplified by treating each event separately.