What do independent events represent in probability?

Independent events in probability are defined as two events that do not influence one another. When two events are independent, the occurrence or non-occurrence of one event has no effect on the probability of the other event occurring. This means that the likelihood of both events happening together can be determined by multiplying their individual probabilities. For example, if you flip a coin and roll a die, the result of the coin flip (heads or tails) does not change the probability of rolling a specific number on the die. Therefore, the independence in this scenario illustrates that these events are entirely separable in their probabilities.

In contrast, the other choices describe different kinds of relationships between events. Some events may require that they occur together, which does not reflect independence. Other scenarios involve events that can occur simultaneously but may not be independent, as their occurrence could still influence one another. Lastly, events that depend on one another mean that the probability of one event is affected by the occurrence of another, which again contradicts the definition of independence.