Students explore probability through a carnival spinner game. They calculate theoretical probabilities, run a 20-spin simulation, and compare theoretical and experimental probabilities. This worksheet supports randomization — each student gets unique outcomes on every spin.
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.
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.
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.
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
All 7.SP.C.5 activities →Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. *For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times*.
All 7.SP.C.6 activities →Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
All 7.SP.C.7 activities →Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. *For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected*.
All 7.SP.C.7a activities →Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. *For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?*
All 7.SP.C.7b activities →
More interactive, auto-graded activities on the same standards and topics.
Students explore how theoretical probability applies to real-world weather forecasting by simulating 20 days of rain predictions. They compare their experimental results to the predicted 30% chance of rain and reflect on what probability really means.
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Students will analyze dot plots representing real-world data, such as the ages of students participating in a school carnival. They will answer questions based on these plots. Each student will receive three unique sets of data and questions, encouraging individual analysis and critical thinking.
