Design a fair contiguous mapping of uniform integers \(1\text{--}20\) to teams W, X, Y, and Z with no unused values. State each block and probability.

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Map W to 1-4, X to 5-9, Y to 10-15, and Z to 16-20, yielding 4/20, 5/20, 6/20, 5/20; call it fair.

Use five integers per team but calculate 5/20 = 1/5; call the equal allocation unfair because the claimed probabilities total 4/5.

W = 1–5, X = 6–10, Y = 11–15, Z = 16–20, so each has probability 5/20 = 1/4.

Give each team one integer and ignore 16 values, yielding 1/20 each per draw; call this fair without a reroll rule.

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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: Map equiprobable outcomes to equal participant chances