Free Printable WorksheetMathGrade 7Math Curriculum7.SP.C.8b

7.140 Compound events using tree diagrams Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 7 Math worksheet provides structured practice on 7.140 Compound events using tree diagrams. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

7.140 Compound events using tree diagrams - In multiple-choice items, students select the correct tree diagram for an experiment and choose the correct probability computed from the branches. (CCSS 7.SP.C.8b)

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

Grade 7

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 7.140 Compound events using tree diagrams skill assessments:

Problem 1Difficulty: Mastery

A club has 5 seventh-grade members and 3 eighth-grade members in a drawing. Two names are drawn without replacement, and then a spinner lands winner 1/4 or no winner 3/4. Which option gives a correct tree diagram and the probability of one seventh-grade and one eighth-grade name, then winner?

ATree: first draw seventh 5/8 and eighth 3/8; after seventh, seventh 4/7 and eighth 3/7; after eighth, seventh 5/7 and eighth 2/7; after each two-draw path, winner spinner branches winner 1/4, no winner 3/4; Probability: 15/28

BTree: first draw seventh 5/8 and eighth 3/8; after seventh, seventh 4/7 and eighth 3/7; after eighth, seventh 5/7 and eighth 2/7; the winner spinner branches are shown only after one selected two-draw path; Probability: 15/112

CTree: first draw seventh 5/8 and eighth 3/8; after every first draw, seventh 5/8 and eighth 3/8; after each two-draw path, winner spinner branches winner 1/4, no winner 3/4; Probability: 15/128

DTree: first draw seventh 5/8 and eighth 3/8; after seventh, seventh 4/7 and eighth 3/7; after eighth, seventh 5/7 and eighth 2/7; after each two-draw path, winner spinner branches winner 1/4, no winner 3/4; Probability: 15/112

Solution & Explanation:First find the matching two-draw paths, then include the independent final branch: (15/56 + 15/56) × 1/4 = 15/112.

Problem 2Difficulty: Mastery

A packet has 6 vowel tiles and 8 consonant tiles. Two tiles are drawn without replacement, and then a coin is tossed. Which option gives a correct tree diagram and the probability of exactly one vowel tile, then heads?

ATree: first draw vowel 3/7 and consonant 4/7; after vowel, vowel 5/13 and consonant 8/13; after consonant, vowel 6/13 and consonant 7/13; after each two-draw path, coin branches heads 1/2, tails 1/2; Probability: 48/91

BTree: first draw vowel 3/7 and consonant 4/7; after every first draw, vowel 3/7 and consonant 4/7; after each two-draw path, coin branches heads 1/2, tails 1/2; Probability: 12/49

CTree: first draw vowel 3/7 and consonant 4/7; after vowel, vowel 5/13 and consonant 8/13; after consonant, vowel 6/13 and consonant 7/13; after each two-draw path, coin branches heads 1/2, tails 1/2; Probability: 24/91

DTree: first draw vowel 3/7 and consonant 4/7; after vowel, vowel 5/13 and consonant 8/13; after consonant, vowel 6/13 and consonant 7/13; the coin branches are shown only after one selected two-draw path; Probability: 24/91

Solution & Explanation:First find the matching two-draw paths, then include the independent final branch: (24/91 + 24/91) × 1/2 = 24/91.

Problem 3Difficulty: Mastery

A container has 4 large blocks and 7 small blocks. Two blocks are drawn without replacement, and then a yes-no card is yes 3/5 or no 2/5. Which option gives a correct tree diagram and the probability of two large blocks, then no?

ATree: first draw large 4/11 and small 7/11; after large, large 3/10 and small 7/10; after small, large 2/5 and small 3/5; after each two-draw path, yes-no card branches yes 3/5, no 2/5; Probability: 12/275

BTree: first draw large 4/11 and small 7/11; after every first draw, large 4/11 and small 7/11; after each two-draw path, yes-no card branches yes 3/5, no 2/5; Probability: 32/605

CTree: first draw large 4/11 and small 7/11; after large, large 3/10 and small 7/10; after small, large 2/5 and small 3/5; the yes-no card branches are shown only after one selected two-draw path; Probability: 12/275

DTree: first draw large 4/11 and small 7/11; after large, large 3/10 and small 7/10; after small, large 2/5 and small 3/5; after each two-draw path, yes-no card branches yes 3/5, no 2/5; Probability: 6/55

Solution & Explanation:First find the matching two-draw paths, then include the independent final branch: (6/55) × 2/5 = 12/275.

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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 Grade 7 Math students. It aligns with educational standard 7.SP.C.8b (Primary standard selected for prompt fields in this prompt cell: CCSS 7.SP.C.8b. Skill statement in this prompt cell: In multiple-choice items, students select the correct tree diagram for an experiment and choose the correct probability computed from the branches. Associated standards listed with this skill in this prompt cell: CCSS 7.SP.C.8b. Use this prompt-provided wording as the supporting standard description for this workflow.).