What defines independent events?

Independent events are defined as two events where the occurrence of one does not affect the occurrence of the other. This means that the probability of one event happening remains unchanged regardless of whether the other event occurs. For example, if you flip a coin and roll a die, the outcome of the coin flip does not influence the outcome of the die roll—these events are independent.

In contrast, options that suggest influence between events, such as the first choice, describe dependent events, where the outcome of one event affects the probability of the other. The second option, which mentions a probability of zero, is a misunderstanding of independent events; independent events can have non-zero probabilities. Finally, the fourth option implies that both events must occur at the same time, which is not a requirement for independence.

Overall, understanding independent events is crucial in probability theory, particularly in scenarios where outcomes are not connected, enabling the calculation of joint probabilities through multiplication of individual probabilities.