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Grade 7 · Mathematics · 30 minutes

Unit 3 · Sampling and probability · Lesson 2 of 2

Chance Models with Two Spins

List compound outcomes and compare a probability model with a small experiment.

Mr. S Teaches · Original starter mini-lesson · MS7-MATH-06

Learning objective

Build a sample space for two fair spins and calculate a compound-event probability.

Before you begin

  • Simple fractions
  • Chance from zero to one

Gather your materials

  • Paper and pencil
  • Optional coin or two-color paper spinner

Language to know

sample space
The complete set of possible outcomes.
compound event
An event involving more than one stage or condition.
relative frequency
The observed fraction of trials producing an event.

Understand the concept

A fair two-color spinner has equally likely red and blue outcomes. For two independent spins, order matters: red then blue differs from blue then red. A table organizes every possible pair. A theoretical probability uses the model; an observed relative frequency uses actual or simulated results and need not match in a small trial set.

Teach it step by step

  1. Draw a two-by-two table with first-spin colors as rows and second-spin colors as columns.
  2. List RR, RB, BR and BB; explain the equal-likelihood assumption.
  3. Count outcomes with exactly one red, then divide by the four possible pairs.
  4. Examine a supplied experiment: 20 pairs of spins produced exactly one red 13 times.
  5. Compare 13/20 with the theoretical value and explain why one experiment does not establish an unfair spinner.

Make the thinking visible

Worked example or model response

Exactly one red occurs in RB and BR, so the modeled probability is 2/4 = 1/2. The experiment gives 13/20 = 0.65. A difference in a small set is possible even with a fair spinner.

Guided practice

For two coin tosses, list all outcomes. Find the probability of no heads and of at least one head.

Independent practice

1. For a fair die rolled once and a fair coin tossed once, how many ordered outcomes exist? 2. Find the probability of an even die result and heads. 3. Explain why counting only HH, HT and TT for two tosses is incomplete.

Quick assessment

Is “at least one red” the same event as “exactly one red”? Compare their probabilities in the two-spin model.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: HH, HT, TH, TT. No heads: 1/4. At least one head: 3/4.
  2. Independent 1: 12 outcomes. 2: Three favorable outcomes out of 12 give 1/4. 3: TH is a distinct ordered outcome from HT.
  3. Quick check: At least one red includes RR as well as RB and BR, so its probability is 3/4 rather than 1/2.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use a color-coded tree diagram and physically point to each ordered pair.

Extension challenge

Design a three-stage sample space and compare exact-one and at-least-one events.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

7.SP.C.8.b

Common Core · Grade 7

Represent compound-event outcomes systematically and identify a specified event.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

7.SP.C.7

Common Core · Grade 7

Compare a probability model with observed relative frequency.

Read the official standard ↗

The small example introduces model comparison, not a statistical test of fairness.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.