Free Printable WorksheetMathAlgebra IIMath CurriculumS-MD.1–3

ALG2.217 Probability Distributions and Expected Value Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.217 Probability Distributions and Expected Value. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.217 Probability Distributions and Expected Value - Primary standard selected for prompt fields in this prompt cell: CCSS S-MD.1–3. Skill statement in this prompt cell: Select the equation, function, or model that represents discrete probability distributions, compute expected value and variance, and evaluate games of chance or decisions. Associated standards listed with this skill in this prompt cell: CCSS S-MD.1–3; CA CCSSM S-MD.1–3; MA 2017 S-MD.1–3; NY NGLS S-MD.1–3; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.217 Probability Distributions and Expected Value skill assessments:

Problem 1Difficulty: Mastery
A software team can run a test that costs $300 and prevents all bug-fix costs. Without the test, the number of bugs X has P(0)=0.40, P(1)=0.35, P(2)=0.20, and P(3)=0.05. Each bug costs $600 to fix. What is the expected net value of running the test?
Solution & Explanation:E(X)=0(0.40)+1(0.35)+2(0.20)+3(0.05)=0.90. Expected avoided cost is 600(0.90)=540. Subtract the $300 test cost to get 240.
Problem 2Difficulty: Mastery
For x=1,3,6, a distribution is P(X=x)=c/x. What is Var(X)?
A2
B8/3
C20/3
D4/9
Solution & Explanation:Here c=2/3, giving probabilities 2/3, 2/9, and 1/9. E(X)=2 and E(X2)=20/3, so Var(X)=20/3-4=8/3.
Problem 3Difficulty: Mastery
For x=1,2,4, a distribution is P(X=x)=c/x. Which pair gives c and E(X)?
Ac=4/7, E(X)=12/7
Bc=7/4, E(X)=12/7
Cc=4/7, E(X)=4
Dc=1/7, E(X)=12
Solution & Explanation:The sum 1+1/2+1/4 is 7/4, so c=4/7. The mean is 1(4/7)+2(2/7)+4(1/7)=12/7.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard S-MD.1–3 (Primary standard selected for prompt fields in this prompt cell: CCSS S-MD.1–3. Skill statement in this prompt cell: Select the equation, function, or model that represents discrete probability distributions, compute expected value and variance, and evaluate games of chance or decisions. Associated standards listed with this skill in this prompt cell: CCSS S-MD.1–3; CA CCSSM S-MD.1–3; MA 2017 S-MD.1–3; NY NGLS S-MD.1–3; TX TEKS Algebra II: §111.40.).

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