If the events $A$ and $B$ are independent and the events $B$ and $C$ are independent, does this necessarily mean events $A$ and $C$ are independent?
I used coin tosses to try to model this with $A = H$, $B = T$, and $C = H$ in separate fair tosses.
I get that they are independent, but am not sure if I am correct.
I also have problems determining if $B$ is independent to $A\cap C$ and also $A \cup C$.