Carnival Game Probability: Is It Really Fair?
In this worksheet, students explore the fundamental concept of comparing theoretical and experimental probabilities. They begin by calculating the mathematical (theoretical) probabilities of different outcomes in a game scenario and then test those expectations by running a 20-spin simulation of the same game.
Through this process, students see how randomness in short experiments can cause results to differ from the expected values — and how increasing the number of trials can bring results closer to the theoretical model.
To make the experience engaging, students are placed in a fun storyline:
🎡 You’ve been hired by a traveling carnival to analyze their popular Prize Spinner game. Your job is to determine if the game is fair by analyzing the probability of winning each prize and comparing it with what really happens when players spin the wheel.
After calculating the probabilities, students simulate spinning the wheel 20 times using a randomized spinner, record their outcomes, and compute experimental probabilities. They then analyze how close these results are to the theoretical values and reflect on why differences may occur.
🧪 In This Worksheet, Students Will:
- Calculate theoretical probabilities for each possible outcome in a spinner game.
- Run a randomized 20-spin simulation and record results.
- Create an experimental probability table based on actual outcomes.
- Compare theoretical and experimental probabilities.
- Reflect on how randomness and sample size impact real-world results.
- Judge whether the game is fair based on mathematical evidence.
Learning Objective
Students will explore the difference between theoretical and experimental probability by analyzing a carnival spinner game. They will calculate expected probabilities, simulate outcomes through randomized trials, compare results, and evaluate the fairness of the game. This activity helps students understand how probability models apply to real-world situations and how randomness affects outcomes.
Randomization Available
Each student’s spinner results are uniquely randomized — every spin produces a different outcome based on the probability model (2/8 Try Again, 3/8 Small Prize, 2/8 Medium Prize, 1/8 Jackpot). Students must record each randomized result, and their responses are auto-graded based on the outcomes they receive.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
