Back to Use probabilities to make fair decisions — Problem 3 · Task Set 33

Exercises: Use Probabilities to Make Fair Decisions

Work through each section in order. A decision procedure is FAIR when every option has exactly the same probability of being chosen. For design problems, describe the mapping and state each option's probability. When a device's outcomes do not divide evenly among the choices, use a divisible range or rejection sampling (reject the leftover outcomes and redraw), and verify each choice has probability $\frac{1}{k}$.

Grade 11·19 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-md-b-6

Work through problems with immediate feedback

Warm-Up: What Makes a Decision Fair

These problems review the meaning of a fair decision.

A fair six-sided die is used to choose fairly among 3 people. Two faces are assigned to each person: person X gets $\{1, 2\}$ , person Y gets $\{3, 4\}$ , person Z gets $\{5, 6\}$ . What is each person's probability of being chosen?

Each person has probability $\frac{2}{6} = \frac{1}{3}$ .

Each person has probability $\frac{1}{6}$ , one per face.

The procedure is unfair because the faces have different numbers.

Person Z has the highest probability because $\{5, 6\}$ are the largest faces.