Skip to content
Brainsladder

Represent Sample Spaces for Compound Events

Students represent sample spaces for compound probability events using organized lists, tables, and tree diagrams. They use these representations to identify all possible outcomes and compute probabilities of specific compound events involving two or more stages.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Represent Sample Spaces for Compound Events

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

Ivy flips a coin and spins a spinner. The grid shows the whole sample space. How many different outcomes are in it?

Count the outcomes.

How it is taught

0:00 of 4:04

A tree diagram shows every path through the stages.

Equal first-stage branches split the same way at the next stage.

Read it: Sample spaces as grids

Roll two dice and every outcome is one cell of a 6 by 6 grid: 6 × 6 = 36 outcomes. A sum of 7 holds 6 of them, 1,6 2,5 3,4 4,3 5,2 and 6,1, so P = 6/36 = 1/6.

  1. Draw the grid: one die's faces down the side, the other's across the top.
  2. Count every cell: the rows times the columns.
  3. Count the event's cells; P is that count over all of them.

Every face of one die meets every face of the other, so the grid holds 6 × 6 cells.

3,4 and 4,3 are different outcomes: the first die shows 3 in one and 4 in the other.

Every cell is equally likely, so P is the event's cells over all 36: 6/36 = 1/6.

The sample space is the rows times the columns; an event is the cells that fit it.

Counting 3,4 and 4,3 as one outcome: 3 cells instead of 6.

They are two cells of the grid, so a sum of 7 holds 6 outcomes.

A 3-section spinner is spun twice. How many outcomes are in the sample space? — 9. Every one of the 3 outcomes of the first meets all 3 of the second: 3 × 3 = 9.

Flip a coin · Spin a 3-color spinner

Sometimes two things happen together. We flip a coin AND spin a spinner — what are all the things that could happen?

A tree diagram helps us see every possibility. Every path begins at one starting dot.

First branch: the coin can land heads or tails.

If we got heads, the spinner can land on red, blue, or green.

Same three colors branch off tails.

Now read each path: heads-red, heads-blue, heads-green, tails-red, tails-blue, tails-green.

Two coin sides times three colors makes six outcomes in all.

What's the chance of getting heads AND red? That's just this one path.

One favorable path out of six total — so the probability is one-sixth.

Coin + Spinner — what could happen?Two stages. Many possibilities.CoinSpinnerOutcomeStartHTRBGRBG(H, R)(H, B)(H, G)(T, R)(T, B)(T, G)2 × 3 = 6 outcomesP(H and R) = 16P(H and R)161 path of 6
Grade 7 · Use a tree diagram to list every outcome

A tree diagram shows every possible outcome, and lets us count them fast.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free