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 choicesAnswer 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