I've seen examples (more appropriately, counter-examples) which show that:
Mutual independence does not imply pairwise independence and vice versa.
I've tried looking around for examples where events are neither pairwise or mutually independent. I couldn't find any so I came up with some examples. To keep things simple, I restricted them to only 3 events. I began to think that at least one pair had to be disjoint (it's sufficient though) in order for the 3 events to be neither mutually or pairwise independent but this wasn't the case.
Question: Is it common for events to be neither mutually or pairwise independent?