Use probabilities to make fair decisions in more complex settings.
List ordered path probabilities and test equal-outcome fairness
Problem
A spinner has color probabilities red \(1/2\), blue \(1/3\), and green \(1/6\), then a fair two-number die is rolled. Compute the six color-number path probabilities and evaluate equal-outcome fairness.
Big Picture
What this problem is really about
Complete ordered paths are the outcomes of a two-stage spinner-and-die process. We’ll multiply each color probability by one-half for each die result, list all six paths, and verify their total is one. The differing color weights carry into the path probabilities, so equal die chances do not make every combined outcome equally likely.
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