Tree Diagrams and Outcome Lists

Tree Diagrams and Outcome Lists — Compound Event Probability (7.SP.C.8a)

An interactive, self-checking probability worksheet where students construct the sample space instead of being handed it.

Most compound probability worksheets give students a finished tree and ask them to read numbers off it. This one works the other way around. Students label every leaf themselves, and the tree fills in as they type — so a missing outcome or a duplicated one becomes visible immediately, in the diagram, before it turns into a wrong answer three questions later.

What students do

Three scenarios, each with a complete tree diagram to build and a set of probability questions:

• Snack Combo — a two-stage lunch choice (drink, then fruit), 6 outcomes. Students mark which outcomes make up each event using an interactive marking tool.
• Three Coin Flips — one coin flipped three times, 8 outcomes. Reinforces that order matters: HHT, HTH, and THH are three different outcomes, not one.
• Uniform Day — shirt colour and shoes, 6 outcomes. Consolidates counting whole branches versus single leaves.

Every problem follows the same two steps: build the sample space, then find the fraction of outcomes that make each event happen.

Why teachers use it

• Self-checking with instant feedback. Students see a green check or a red mark on every entry. No answer key to distribute, no grading pile.
• Fractions stay unsimplified (3/6, not 1/2) so the numerator and denominator remain visible as the count of matching outcomes over the size of the sample space — which is exactly what the standard assesses.
• Deliberately paired questions teach complements and shortcuts without a formula: "exactly two heads" sits next to "at least two heads," and "P(black shoes)" sits next to "P(brown shoes)."
• A one-sentence summary after each problem names the transferable idea so the three exercises add up to one concept.
• Fits a single class period. Roughly 20 minutes of student work.

Standards alignment

• 7.SP.C.8a — Understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
• 7.SP.C.8b — Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams.

What's included

• Interactive digital worksheet, three problems, 20 probability questions
• Three-slide introduction deck for whole-class projection, with speaker notes
• Teacher tips and a common-mistakes list
• Step-by-step student instructions
• Complete answer key

Great for

7th grade math, pre-algebra, probability and statistics units, compound events lessons, sample space practice, tree diagram practice, math intervention and small-group work, sub plans, homework, distance learning, and test prep.

Keywords: tree diagrams, sample space, compound events, compound probability, organized list, outcome list, counting outcomes, 7th grade probability, 7.SP.C.8a, 7.SP.C.8b, interactive math worksheet, self-checking, digital math activity, no prep, middle school statistics and probability.