Independence is a confusing concept. Is independence intuitive or  not? Is the multiplicative rule for independence a sufficient condition or a necessary-and-sufficient condition? What does symbol used in independence of simultaneous occurrence events express and how do we interpret it? This paper probes the cause for these confusions and insists that independence would be expanded because of the use of the same symbol (intersection) in both simultaneous occurrence events and compatible events. Also, symbols, meaning, and object (events) of independence are analyzed from the perspective of Peirce’s Semiotic and of Skemp. Although the result says that confusion is unavoidable, teachers should recognize the expanded independence for teaching it properly and encourage students to use symbols with explicit meaning.

independence, probability.