Back to Use probabilities to make fair decisions — Problem 1 · 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

Fluency Practice

Judge whether each procedure is fair and design simple fair mappings.

A coin is biased: it lands heads $70\%$ of the time and tails $30\%$ of the time. It is used to decide between two people (heads for one, tails for the other). Is this procedure fair?

No — it uses chance but the two outcomes are not equally likely, so it is not fair.

Yes — any coin flip is fair because it is random.

Yes — heads and tails are still two different outcomes.

It cannot be decided without flipping the coin many times.