An independent event is a situation in probability where the outcome of one event does not affect the outcome of another. For example, if you flip a coin and roll a die, the result of the coin flip (heads or tails) has no impact on the number rolled on the die. Each event occurs separately, and their probabilities remain unchanged regardless of each other. In mathematical terms, two events A and B are independent if the probability of both occurring together is equal to the product of their individual probabilities. This can be expressed as P(A and B) = P(A) × P(B). Understanding independent events is crucial in fields like statistics and gambling.