Independent Events in a Simple Random Experiment and the Meaning of Independence

TL;DR

This paper investigates the structure of independent events in a finite sample space involving coin flips and die rolls, highlighting open questions and proposing potential approaches for further research.

Contribution

It provides a detailed count and pattern analysis of independent events in a simple experiment, revealing open questions about their structure.

Findings

Counted 888,888 pairs and tuples of independent events

Identified open questions about the structure of independence

Suggested possible approaches for future research

Abstract

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.