What are dependent events in probability?

Dependent events in probability are defined as events where the occurrence or non-occurrence of one event influences the probability of another event occurring. For example, consider drawing two cards from a deck without replacement. The probability of drawing a second card is affected by the outcome of the first draw; if the first card drawn is an ace, the probability of drawing another ace changes. This demonstrates that the two events are connected, making them dependent.

In contrast, independent events, where the outcome of one event does not influence the other, might be exemplified by tossing a coin and rolling a die. The outcome of one does not affect the outcome of the other. Thus, recognizing the interdependent relationship among events is crucial in determining their probabilities accurately.