Probability and Statistics — Free Algebra 2 Review Games.
This unit covers permutations and combinations, binomial probability and normal distribution — essential concepts for Algebra 2. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers permutations and combinations, binomial probability and normal distribution — essential concepts for Algebra 2. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Permutations and Combinations
Permutations count arrangements where order matters; combinations count selections where order does not matter. Students must know when to apply each formula and how to handle factorial expressions. The formulas are nPr = n! / (n-r)! and nCr = n! / (r!(n-r)!).
Key Points
- Use permutations when order matters (e.g., rankings, passwords, seating arrangements)
- Use combinations when order does not matter (e.g., choosing a committee, selecting items)
- n! means the product of all positive integers from 1 to n; 0! = 1
- nCr is also written as C(n,r) or the binomial coefficient notation
A class of 10 students needs to elect a president, vice president, and secretary. How many different outcomes are possible?
Order matters here because each position is different, so use permutations: 10P3 = 10! / (10-3)! = 10! / 7! = 10 × 9 × 8 = 720. If instead you were just choosing 3 students for a committee (no specific roles), you would use 10C3 = 10! / (3! × 7!) = 120.
2 Binomial Probability
Binomial probability applies when there are exactly two outcomes (success/failure), a fixed number of trials, and each trial is independent with the same probability of success. The formula is P(X = k) = C(n,k) × p^k × (1-p)^(n-k). Students must correctly identify n, k, and p from a word problem.
Key Points
- n = total number of trials, k = number of successes, p = probability of success on one trial
- The combination C(n,k) counts how many ways k successes can be arranged among n trials
- P(at least one) = 1 - P(none) is a common shortcut on exams
- Mean of a binomial distribution: μ = np; standard deviation: σ = √(np(1-p))
A multiple-choice quiz has 5 questions, each with 4 answer choices. If a student guesses randomly on every question, what is the probability of getting exactly 3 correct?
Here n = 5, k = 3, and p = 1/4 = 0.25. Plug into the formula: P(X = 3) = C(5,3) × (0.25)^3 × (0.75)^2. C(5,3) = 10, (0.25)^3 = 0.015625, and (0.75)^2 = 0.5625, giving 10 × 0.015625 × 0.5625 ≈ 0.0879, or about 8.8%.
3 Normal Distribution
The normal distribution is a symmetric, bell-shaped curve defined by its mean (μ) and standard deviation (σ). Students must be able to use the Empirical Rule (68-95-99.7) and calculate or interpret z-scores to find probabilities and percentiles. On exams, problems typically require converting raw scores to z-scores and using a z-table or calculator.
Key Points
- Empirical Rule: 68% of data falls within 1σ, 95% within 2σ, 99.7% within 3σ of the mean
- Z-score formula: z = (x - μ) / σ; a z-score measures how many standard deviations a value is from the mean
- A positive z-score is above the mean; a negative z-score is below the mean
- To find the percent of data above a value, compute the z-score then subtract the table area from 1
The scores on a history test are normally distributed with a mean of 74 and a standard deviation of 8. What percentage of students scored between 66 and 90?
Convert each score to a z-score: z = (66 - 74) / 8 = -1 and z = (90 - 74) / 8 = 2. Using the Empirical Rule, 68% of data falls within 1 standard deviation (between 66 and 82), and 95% falls within 2 standard deviations (between 58 and 90). The area from z = -1 to z = 2 is approximately 68%/2 + 95%/2 = 34% + 47.5% = 81.5% of students.
Questions, answered.
What is Probability and Statistics?
Probability and Statistics is Unit 10 of Algebra 2, covering permutations and combinations, binomial probability and normal distribution.
How to study for Algebra 2 Unit 10?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 27+ review questions across 5 different game modes.