Use probabilities to make fair decisions in more complex settings.
List ordered path probabilities and test equal-outcome fairness
Problem
A fair coin is followed by a fair six-sided die, and each ordered pair (coin result, die number) is a fairness target. Compute every ordered-outcome probability and evaluate fairness across the \(12\) outcomes.
Big Picture
What this problem is really about
For a multistage chance process, the basic objects are complete ordered paths, not the outcomes from either stage by itself. Multiply the branch probabilities along one path, then repeat for every path in the stated fairness group. Fairness is decided only after those final path probabilities are compared and their total accounts for the whole process.
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