Use probabilities to make fair decisions in more complex settings.
Identify and test the hidden equiprobability assumption
Problem
A rule claims that sums \(2\text{--}12\) from two fair dice are equally likely. Analyze the equal ordered pairs, compare the path counts for sums \(7\) and \(2\), and evaluate the claim.
Big Picture
What this problem is really about
A list of named results is not automatically a list of equally likely outcomes. Trace each name back to the genuinely equiprobable atomic outcomes, then count how many atoms feed each category. If those category counts differ, equal treatment of the category labels rests on a hidden assumption that the model does not support.
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