Expected Outcomes
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice finding the expected value of a discrete probability distribution and explaining what that number means in the long run. Students work through six situations involving arcade tickets, daily orders, game points, defective items, contest prizes, and goals scored.
Each problem gives possible values of the random variable and the probability of each value. Students multiply each outcome by its probability, add the results, and then describe the final number as a long-run average.
What Students Practice
Students practice calculating expected value by weighting each possible outcome according to how likely it is. Outcomes that are more likely have a larger influence on the final average.
The worksheet also asks students to interpret the answer. For example, an expected value of 2.4 does not mean the experiment will literally produce 2.4 items on one trial. It means that over many repeated trials, the average result would be about 2.4.
Why This Skill Matters
Expected value is one of the most useful ideas in probability because it summarizes the long-run center of a distribution. It is used in games, insurance, finance, business, and decision-making.
Students also learn an important idea about averages: an expected value does not have to be one of the actual possible outcomes. It represents a long-run average, not necessarily a result from one single trial.
Common Challenges
Students may add the outcomes and probabilities separately instead of multiplying each pair first. Remind them that every outcome must be weighted by its own probability.
Another common mistake is thinking the expected value is guaranteed to happen. Encourage students to describe it as an average over many repetitions.
How To Use It
Teachers can use this worksheet after students are comfortable reading probability distributions. It works well for guided examples, independent practice, homework, or a real-world probability lesson.
Parents and homeschool teachers can explain expected value as “the average result we would expect if we repeated the situation many, many times.”
Grade Alignment
This Grade 12 Pre-Calculus worksheet supports understanding of expected value for discrete probability distributions and long-run averages.
Students should already know how to read a probability table and multiply decimals. After this practice, they can move into mean and standard deviation of a distribution.