Uniform accepted digits are \(0\text{--}7\), and each of four students receives two digits. Compute each student's conditional probability and evaluate fairness.

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Give each student probability 1/4 because there are four students; call the rule fair without checking the two accepted digits per student.

Each student has probability 2/8 = 1/4, so the rule is fair conditional on uniform accepted digits.

Give each student probability 2/8 = 1/4, but call the rule unfair because digits 8 and 9 are outside the accepted uniform set.

Give each student probability 2/10 = 1/5; the four probabilities total 4/5, but call the rule fair.

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Curriculum context

Course: Math III
Standard: S-MD.6
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Use probabilities to make fair decisions in more complex settings.
Problem type: Compare participant probabilities under an explicit fairness rule