Independent Events in a Simple Random Experiment and the Meaning of   Independence
  We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first number, equal to 888,888, suggest that there are some open questions about the structure of independence even in a finite sample space. We discuss briefly these questions and possible approaches to answer them. 
Isaac M. Sonin
math.PR math.CO