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Common Core Math7th GradeStatistics & Probability

7.SP.8: Probability of Compound Events

Also written as 7.SP.C.8 and CCSS.MATH.CONTENT.7.SP.C.8 · Cluster: Investigate chance processes and develop, use, and evaluate probability models.

Make Compound Probability ProblemsAll 24 7th Grade Math Standards

The Official Wording

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Common Core State Standards, Grade 7, Statistics & Probability · Read it at the source · Checked October 14, 2026

What 7.SP.8 Means in Plain English

Seventh graders find probabilities of events built from two or more steps. For a family with three children, a tree diagram lists all 8 equally likely outcomes, GGG through BBB, and exactly two girls happens in 3 of them, so the probability is 3/8.

Part c adds simulation: toss three coins 40 times, heads for a girl, and about 15 tosses should show exactly two heads. 8th grade organizes paired categories in two-way tables (8.SP.4), and high school adds independent events (HSS-CP.2).

7.SP.8 I Can Statements

  • I can list a sample space with a table, list or tree diagram.
  • I can find a compound probability as a fraction of the outcomes.
  • I can design a simulation to estimate a compound probability.

7.SP.8 Worked Example

One question answered by counting branches (parts a and b) and then by tossing coins (part c), so the two answers can be compared.

Problem

A family has three children. Assume each child is equally likely to be a girl or a boy. What is the probability of exactly two girls? Find it with a tree diagram, then design a simulation to check it.

Exactly two girls out of three children
  1. (b) Build the sample space with a tree: each child branches into G or B, three levels deep.GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB: 8 outcomes
  2. (b) Mark the outcomes that make up the event “exactly two girls.”GGB, GBG, BGG
  3. (a) The probability is the fraction of the sample space where the event happens.P(exactly 2 girls) = 3/8 = 0.375
  4. (c) Design a simulation with the same chances: a coin is heads or tails with probability 1/2 each, like a girl or a boy. Toss three coins together as one family, 40 times.Heads = girl, tails = boy; 40 trials of 3 coins
  5. (c) Count the trials with exactly two heads and compare. One class got 14.14/40 = 0.35, close to 0.375 (expected 3/8 × 40 = 15)
Answer3/8, since 3 of the 8 equally likely outcomes have exactly two girls; the simulation gave 14/40 = 0.35, close to it

Check it: Count the sample space another way: 2 choices for each of 3 children is 2 × 2 × 2 = 8 outcomes. The event “at least two girls” adds GGG, giving 4/8, which should be larger than 3/8, and it is.

Common Mistakes with 7.SP.8

Listing outcomes that are not equally likely

A family has 0, 1, 2 or 3 girls, so P(2 girls) = 1/4

Try this: List the outcomes in birth order with a tree: 8 equally likely branches, and three of them give exactly two girls.

Missing outcomes in an unorganized list

GGB, BGG, GGG, BBB, BBG, GBB: 6 outcomes

Try this: Use a tree or fixed order so nothing is skipped, and check the count: 2 × 2 × 2 = 8, not 6.

Simulating with the wrong chances

Roll a number cube: 1 means a girl, 2 to 6 means a boy

Try this: Match each simulated outcome’s chance to the real one: a girl is 1/2, so use a coin, or even and odd on the cube.

Where 7.SP.8 Fits

Comes Before5.NF.4Multiply fractions, like ½ × ½ × ½ = ⅛, the chance of one branch.
Alongside7.SP.7Probability models, where each branch of a tree is one outcome.7.SP.6Long-run relative frequency, which a simulation produces.
Comes Next8.SP.4Two-way tables of paired categories and their relative frequencies.
HSS-CP.2Independent events, where the probability of both is the product.

Practice 7.SP.8

Word Problem GeneratorFree ToolCoin, spinner and number cube problems with two or three stages, where students build the sample space before counting.ProbabilityCompound eventsGrade 7
Make Word Problems
Graph Paper GeneratorFree ToolGrid paper for a 6 by 6 table of two number cubes, one outcome per square: 36 squares, and an event is the squares you shade.Large squaresLetterPrint
Make Graph Paper

Quick Check

  1. Two number cubes are rolled. What is the probability of rolling double sixes?
  2. Two number cubes are rolled. What is the probability that the sum is 7?
  3. A coin is tossed and a spinner with red, blue and green equal sections is spun. What is P(heads and red)?

7.SP.8: Other Names

7.SP.87.SP.C.8CCSS.MATH.CONTENT.7.SP.C.8

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.