Difference between independent and dependent events in probability theory

Independent events are events where the occurrence of one event does not affect the occurrence of the other event. In other words, the outcome of one event has no impact on the outcome of the other event. For example, flipping a coin and rolling a die are independent events.

On the other hand, dependent events are events where the occurrence of one event does affect the occurrence of the other event. In other words, the outcome of one event is dependent on the outcome of the other event. For example, drawing a red card from a deck of cards and then drawing another card without replacing the first card are dependent events.

Understanding the difference between independent and dependent events is crucial in probability theory as it helps in accurately calculating the probabilities of various outcomes.