Problem preview

S-MD.6 Warmup M2-072-A09-V02

Use probability to make fair decisions, such as lotteries or random selection.

Decide whether a multi-stage random selection process is fair by comparing each participant's overall probability

Problem

For a person in a grade of size \(g\), multiply the tree branches \(g/12\) and \(1/g\). Compare the resulting person-level probability across grades.

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It is not fair because people in larger grades are less likely to be chosen, since there are more people competing for the one spot in that grade.

It is fair because a grade with g people is chosen with probability g/12, then each person in that grade has probability 1/g, so each person’s overall chance is 1/12.

It is fair because once a grade is chosen, every student in that grade is selected uniformly, so the whole process must give everyone the same chance.

It is not fair because choosing grades first makes the grades equally important, so students in smaller grades end up with a better chance overall.

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Curriculum context

Course: Math II
Standard: S-MD.6
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Use probability to make fair decisions, such as lotteries or random selection.
Problem type: Decide whether a multi-stage random selection process is fair by comparing each participant's overall probability