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

Fluency Practice

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

A random number generator produces integers from 1 to 100, each equally likely. To choose between two people, the blocks are: person P gets $1$ – $50$ , person Q gets $51$ – $100$ . Is this procedure fair?

Yes — each block has 50 of the 100 equally likely integers, so each probability is $\frac{50}{100} = \frac{1}{2}$ .

No — a computer generator can never be trusted to be fair.

No — the numbers $51$ – $100$ are larger, so person Q is favored.

It is fair only if you also flip a coin afterward.