When are events considered independent in probability?

In probability theory, events are considered independent when the occurrence of one event does not influence the likelihood of the occurrence of another event. This means that knowing whether one event has occurred gives no information about whether the other event will occur. For instance, flipping a coin and rolling a die are independent events; the result of the coin flip does not affect the outcome of the die roll.

Understanding this definition is crucial because it underpins various probability calculations, such as determining the likelihood of multiple independent events happening together. When the independence of events is established, the joint probability can be calculated by simply multiplying the probabilities of the individual events.

The assessment of independence is key in probability, as it allows for simplifications in calculations and a clear understanding of how different events relate to one another, or in this case, do not relate.