Exact Binomial
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice finding the probability of one exact number of successes in a binomial experiment. Students work through six situations involving free throws, game wins, correct answers, acceptable products, mystery prizes, and penalty kicks. Each problem gives the number of trials, the chance of success, and the exact number of successes to find.
The worksheet also gives students the binomial probability formula so they can focus on using it correctly. Students substitute the values from the situation into the formula, simplify, and round the final probability to four decimal places.
What Students Practice
Students practice identifying the number of trials, the probability of success, and the exact success count. They then use those values in the binomial formula to calculate one specific probability.
The worksheet reinforces the difference between an exact probability and a cumulative probability. If a problem asks for exactly four successes, students only calculate the probability for four, not four or more and not four or fewer.
Students also get practice using combinations, powers, and calculator technology in a probability setting.
Why This Skill Matters
Exact binomial probability is one of the main tools students use when working with repeated independent trials. It allows them to answer questions such as the chance of making exactly four shots, getting exactly six correct answers, or finding exactly a certain number of defective products.
This skill also builds the foundation for cumulative probability. Before students can find the chance of several possible outcomes together, they need to understand how one exact outcome is calculated.
Common Challenges
Students may confuse the total number of trials with the number of successes being requested. Encourage them to identify both values separately before using the formula.
Another common mistake is using the probability of failure where the success probability belongs. Students should first decide what the problem is calling a success, then use the matching probability.
Students may also forget that the failure probability is the part left over after success. If success is 60 percent, failure is 40 percent.
How To Use It
Teachers can use this worksheet after students understand the conditions of a binomial experiment and can identify the model parameters. It works well for guided examples, independent practice, homework, or calculator review.
Parents and homeschool teachers can ask three questions first: “How many trials are there? What is the chance of success? How many successes do we want exactly?” Once those are clear, students can place the values into the formula.
Grade Alignment
This worksheet is designed for Grade 12 Pre-Calculus students studying probability distributions. It builds fluency with exact binomial probabilities and prepares students for cumulative binomial calculations.
Students should already understand combinations, powers, and basic probability. After this practice, they are ready to calculate probabilities involving ranges of success counts.