Free Printable WorksheetMathGeometryMath CurriculumG-MG.A.1

GEO.180 Use geometric probability models when included Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.180 Use geometric probability models when included. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.180 Use geometric probability models when included - Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.1. Skill statement in this prompt cell: Select the correct geometric probability setup using area or length ratios and compute the probability. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1; CCSS SMP.4, G-MG.A; MA 2017 Modeling; TEKS Process. Use this prompt-provided wording as the supporting standard description for this workflow.

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

Geometry

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 GEO.180 Use geometric probability models when included skill assessments:

Problem 1Difficulty: Mastery
A circular target has radius 20 units. Four disjoint shaded annular sectors are each 40 degrees and lie outside a concentric inner circle of radius 10 units. A dart hits the whole target uniformly at random. What is the probability that it lands in one of the shaded sectors?
A1/3
B2/9
C4/9
D3/4
Solution & Explanation:The four sectors have total angle 4 x 40 = 160 degrees. The annular part outside radius 10 has area ratio (202 - 102)/202 = 300/400 = 3/4. The probability is (160/360)(3/4) = (4/9)(3/4) = 1/3.
Problem 2Difficulty: Mastery
In the rectangle 0 <= x <= 14 and 0 <= y <= 10, a point is chosen uniformly at random. What is the probability that the point is below or on the line through (0,2) and (14,8), or above the line y = 8?
A4/5
B9/14
C1/2
D7/10
Solution & Explanation:The region below the line through (0,2) and (14,8) is a trapezoid with bases 2 and 8 and height 14, so its area is (1/2)(2 + 8)(14) = 70. The region above y = 8 has area 14 x 2 = 28. These regions do not overlap in area, so the union area is 98. The rectangle area is 140, so P = 98/140 = 7/10.
Problem 3Difficulty: Mastery
A point is chosen uniformly on the circumference of a circle with radius 10 units. Two marked arcs have lengths 5pi and 7pi. What is the probability that the point is on a marked arc?
A12/100
B3/5
C7/10
D5/12
Solution & Explanation:The circle circumference is 2pi(10) = 20pi. The marked arc length is 5pi + 7pi = 12pi, so P = 12pi/20pi = 3/5.

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Frequently Asked Questions

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Yes! In addition to this printable worksheet, students can practice GEO.180 Use geometric probability models when included interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-MG.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.1. Skill statement in this prompt cell: Select the correct geometric probability setup using area or length ratios and compute the probability. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1; CCSS SMP.4, G-MG.A; MA 2017 Modeling; TEKS Process. Use this prompt-provided wording as the supporting standard description for this workflow.).

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