Distribution Audit Answer Key

About This Worksheet

This worksheet helps twelfth-grade Pre-Calculus students practice checking whether a discrete probability distribution is valid. Students work through ten small probability tables and decide whether each one can represent a real probability distribution. If a table is not valid, they explain what is wrong.

The two main rules are straightforward. Every probability must be between zero and one, and all of the probabilities in the table must add up to one. Students use those rules to inspect each distribution carefully.

What Students Practice

Students practice adding the listed probabilities and checking whether the total is exactly one. They also look for individual probabilities that are negative or greater than one, since either of those would make the distribution invalid.

The worksheet includes some distributions that are correct and others that fail for different reasons. This helps students learn to check both rules instead of stopping after only one.

Why This Skill Matters

Before students use a probability distribution to find an expected value or standard deviation, they need to know that the distribution itself makes sense. A bad distribution will lead to bad calculations.

This skill also builds good checking habits. Students learn that probability models have rules, and those rules can be used to catch errors quickly.

Common Challenges

Students may only check whether the probabilities add to one and forget to inspect each individual value. Remind them that both conditions matter.

Another common mistake is thinking a total very close to one is automatically valid. On this worksheet, students should use the values exactly as written and decide whether the total really equals one.

How To Use It

Teachers can use this worksheet after students have built a few simple probability distributions. It works well for independent practice, homework, partner checking, or a quick review before expected value.

Parents and homeschool teachers can ask two questions: “Are all the probabilities between zero and one?” and “Do they all add up to one?” If both answers are yes, the distribution is valid.

Grade Alignment

This worksheet is designed for Grade 12 Pre-Calculus students studying discrete probability distributions. It supports accurate interpretation and validation of probability models.

Students should already understand simple probability tables. After this practice, they are ready to solve for a missing probability.