The penny arcade gets the statistics treatment in this fun probability investigation. A non-standard game of chance is described and then the class is set loose to find missing probabilities, determine common outcomes, and evaluate frequency. A great activity for multi-level classes, as each problem is solvable by both brute force and more elegant methods. With some reformatting, it would also make for an excellent open-response practice.

Concepts

compound probability, experimental probability, statistics

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Additional Tags

math

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Instructional Ideas

• Have the class develop a game that fits the model described and run a simulation
• Compare the probabilities detailed here to actual games of chance, like a roulette wheel
• Investigate and determine what minimum monetary value a ticket needs to have for this to be a player-favoring game

Classroom Considerations

• Probability chart is too small for filling in directly, perhaps enlarge while copying or give instructions to record answers on a separate sheet
• Consider that some districts may have policies regarding studying games of chance

Pros

• Each problem has multiple solution paths
• Excellent practice distinguishing point and cumulative probabilities
• Problems build logically without relying on previous answers for completion

Cons

• A diagram and more complete game description is available in the original exercise "Fred's Fun Factory", but no link to this exercise is provided
• Student worksheet, teaching directions, and answer key are not clearly separated

Common Core

HSS-CP.A.1 HSS-CP.A.2