Game Fairness Answer Key
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice using expected value to decide whether a game is favorable, fair, or unfavorable to the player. Students work through five game situations involving prizes, bonuses, spinners, cards, and dice. Each problem gives the possible gains or losses and the probability of each outcome.
Students calculate the expected gain or loss for each game and then classify the result. A positive expected value means the game is favorable to the player in the long run. An expected value of zero means the game is fair. A negative expected value means the game is unfavorable.
What Students Practice
Students practice multiplying each possible gain or loss by its probability and then adding those results together. They must pay close attention to signs because losses are represented as negative values.
The worksheet also asks students to interpret the expected value instead of stopping with the calculation. This helps them connect the number with what it means for someone who plays the game many times.
Why This Skill Matters
Expected value is one of the most useful tools for judging games and financial decisions. A game can offer a large prize and still be unfavorable if the chance of winning is very small.
This skill also teaches students to look beyond one lucky or unlucky outcome. Expected value focuses on the long-run average, which is often a better way to judge whether a game is fair.
Common Challenges
Students may treat a loss as a positive amount. Remind them that money lost should enter the expected-value calculation as a negative value.
Another common mistake is assuming a game with a possible jackpot must be favorable. Students need to consider both the size of each outcome and how likely it is.
How To Use It
Teachers can use this worksheet as an applied expected-value lesson or as a final activity for a probability-distributions unit. It works well for independent work, homework, group discussion, or a game-analysis lesson.
Parents and homeschool teachers can explain it this way: “If we played this game over and over, would the player average a gain, break even, or lose money?” That is what the expected value tells us.
Grade Alignment
This worksheet is intended for Grade 12 Pre-Calculus students studying expected value and probability distributions. It connects probability calculations with real-world decision-making and game fairness.
Students should already know how to calculate expected value. After this practice, they are ready to use probability models in broader decision and risk situations.