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 9 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 8 students? _____
- 5.How many ordered arrangements of 3 students can be chosen from 8? _____
- 6.For 5 fair coin tosses, find the expected number of heads: _____
Show answer key
- Question 1: 84
- Question 2: 210
- Question 3: 2
- Question 4: 56
- Question 5: 336
- Question 6: 2.5
Free Practice Worksheets
Print, solve on paper, then upload a photo for instant AI grading and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Calculate the number of permutations of 6 items taken 2 at a time: P(6, 2)
- 2.Calculate the number of combinations of 8 items taken 3 at a time: C(8, 3)
- 3.Given P(A) = 0.4 and P(B|A) = 0.5, calculate the joint probability P(A and B) using the formula P(A and B) = P(A) * P(B|A)
- 4.Calculate the z-score for a data point x = 110, given a mean (μ) = 100 and a standard deviation (σ) = 5. Use formula: z = (x - μ) / σ
- 5.Calculate the probability of exactly 2 successes in 4 trials (n=4, k=2) where the probability of success p = 0.5, using the binomial formula: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
- 6.Find the predicted y-value for a regression line equation y = 2x + 3 when x = 4
Full range of grade expectations
Solve each problem. Show your work.
- 1.A committee of 4 students is to be chosen from a group of 10 juniors and 8 seniors. How many ways can the committee be formed if it must contain exactly 2 juniors and 2 seniors?
- 2.A machine produces components with a mean diameter of 50mm and a standard deviation of 2mm. Assuming the diameters follow a normal distribution, what is the probability that a randomly selected component has a diameter greater than 54mm? (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 and 7 blue 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.Real-world context: A real estate agent tracks the relationship between the square footage of a house (x) and its selling price in thousands (y). The calculated regression line is y = 0.15x + 50. Predict the selling price of a house that is 2,000 square feet.
- 6.How many distinct ways can the letters of the word 'STATISTICS' be arranged?
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.