Grade 12 Statistics & Probability Worksheets
Free printable statistics & probability practice for Grade 12 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 12 Statistics & Probability Practice
Solve each problem. Show your work.
- 1.How many ways can 3 students be chosen from 7 students? _____
- 2.How many ordered arrangements of 3 students can be chosen from 7? _____
- 3.For 4 fair coin tosses, find the expected number of heads: _____
- 4.How many ways can 3 students be chosen from 9 students? _____
- 5.How many ordered arrangements of 3 students can be chosen from 10? _____
- 6.For 5 fair coin tosses, find the expected number of heads: _____
Show answer key
- Question 1: 35
- Question 2: 210
- Question 3: 2
- Question 4: 84
- Question 5: 720
- Question 6: 2.5
Free Practice Worksheets
Print, solve on paper, then upload a photo for AI feedback and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Calculate the value of the permutation P(7, 2).
- 2.Calculate the value of the combination C(8, 3).
- 3.Given a normal distribution with mean = 50 and standard deviation = 5, find the z-score for a value of 60.
- 4.Find the probability P(X = 2) for a binomial distribution where n = 4 and p = 0.5.
- 5.Given P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2, calculate the conditional probability P(A|B).
- 6.For a linear regression line y = 2x + 3, calculate the predicted y value when x = 4.
A selection of topic skills
Solve each problem. Show your work.
- 1.A committee of 4 people is to be chosen from a group of 10 men and 8 women. How many ways can the committee be formed if it must contain exactly 2 men and 2 women?
- 2.A machine produces components with a mean weight of 500 grams and a standard deviation of 15 grams. If weights are normally distributed, what is the probability that a randomly selected component weighs more than 530 grams? (Use z-scores)
- 3.In a binomial experiment with n=10 trials and a probability of success p=0.4, calculate the probability of getting exactly 3 successes.
- 4.A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn without replacement, what is the conditional probability that the second marble is blue, given that the first marble was red?
- 5.A data set has a correlation coefficient (r) of -0.85. Describe the strength and direction of the relationship between the two variables, and explain what happens to the dependent variable as the independent variable increases.
- 6.In a survey of 100 students, 60 study Mathematics, 40 study Physics, and 20 study both. If a student is chosen at random, what is the probability they study Mathematics or Physics?
What Your Child Will Learn
This course builds a systematic toolkit for counting outcomes and quantifying uncertainty, starting with the fundamental counting principle and progressing to permutations (ordered arrangements) and combinations (unordered selections). Students learn to recognize which counting technique a problem calls for — a distinction that hinges on whether order matters and whether repetition is allowed — and apply factorial notation to compute these counts efficiently.
Probability builds on this counting foundation, covering theoretical and experimental probability, conditional probability, and the difference between independent and dependent events. Students calculate probabilities for compound events using addition and multiplication rules, and interpret probability trees and two-way tables to organize multi-stage scenarios.
The course then moves into probability distributions, focusing on the binomial distribution for repeated independent trials and the normal distribution for continuous data, including z-scores and the empirical (68-95-99.7) rule. Students also study correlation and linear regression as tools for analyzing relationships between two variables, extending the data-analysis ideas from Grade 9 with formal statistical measures like the correlation coefficient. Together, these topics prepare students to critically interpret statistics encountered in research, media, and everyday decision-making.
Skills Covered
- Applying the fundamental counting principle
- Calculating permutations and combinations
- Computing probabilities of independent, dependent, and conditional events
- Working with the binomial probability distribution
- Applying the normal distribution, z-scores, and the empirical rule
- Analyzing correlation and linear regression between two variables
Curriculum Aligned: Core content of Data Management (MDM4U in Ontario), covering combinatorics, probability distributions, and statistical analysis for university programs in business, social science, and health sciences.
Parent Tip: Probability and statistics problems often turn on subtle wording — 'at least one' versus 'exactly one,' or 'with replacement' versus 'without replacement' — so even without checking the math, you can help by reading the problem together and asking your teen to restate exactly what's being asked before they calculate anything.
What your child will practice
- PermutationsSolve problems involving permutations (with and without repetition).
- Normal Probability CalculationsCalculate probabilities using the standard normal distribution table or technology.
- CombinationsSolve problems involving combinations and distinguish between permutations and combinations.
- Probability BasicsCalculate theoretical and experimental probability of events.
- Binomial DistributionCalculate probabilities using the binomial distribution formula.
- Normal DistributionApply the properties of the normal distribution and calculate z-scores.
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Check my workFrequently Asked Questions
How often should my child practice statistics & probability?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.