Final answer:
Two events are independent if one's occurrence doesn't affect the probability of the other's occurrence. Independent events satisfy criteria like P(A AND B) = P(A)×P(B). Mutually exclusive events are different, indicating that both cannot happen simultaneously.
Step-by-step explanation:
Two events are independent if the occurrence of event E in a probability experiment does not affect the probability of event F in the same experiment. This concept is fundamental as it helps to determine if two events can occur simultaneously without influencing each other's outcomes. In probability theory, independent events satisfy certain criteria such as:
- P(A AND B) = P(A) × P(B)
- P(A|B) = P(A)
- P(B|A) = P(B)
On the other hand, events that do not satisfy these conditions are considered dependent events. Moreover, mutually exclusive events are a separate category, indicating that the two events cannot happen at the same time (P(A AND B) = 0). Understanding these definitions is crucial when analyzing situations where multiple outcomes are possible, such as in rolling dice, drawing cards, or random sampling.