What does it mean for two events to be independent in probability?

In probability, two events are considered independent if the occurrence of one event does not affect the likelihood of the other event occurring. For example, if you flip a coin and roll a die, the outcome of the coin flip has no impact on which number you roll. Mathematically, this is represented by the equation P(A and B) = P(A) × P(B), where A and B are the two independent events. Understanding independence in events can greatly simplify problems in probability. One common mistake is assuming that two events are independent simply because they are not related or appear separate, when in fact they might have some hidden correlation. Always check the probabilities and perform calculations to confirm independence—they might surprise you!