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.

Your answer

Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.

A There are 12 ordered outcomes, so assign each probability 1/6; these total 2, so incorrectly call the process fair. B Each ordered outcome has probability 1/12 and the probabilities total 1, but call the process unfair because coin and die results have different labels. C Assign each heads outcome probability 1/6 and each tails outcome 1/12; these total 3/2, so incorrectly call the process fair. D Each of the 12 ordered outcomes has probability 1/12, so the process is fair across those outcomes.

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List ordered path probabilities and test equal-outcome fairness

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Hint

Solution walkthrough

Count the ordered outcomes

Use independence for one pair

Compute and check total probability

Evaluate fairness

Another way

Common mistake

Solution walkthrough video