Good Learning Co.
SavannahYear 8
← Maths
MathsProbability and data30 min★★★ difficulty

Listing outcomes with tables and Venn diagrams

Most probability marks are lost by missing an outcome, not by getting the arithmetic wrong. Being systematic is the actual skill.

Lesson overview

What you'll learn in this lesson

Enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams

Key learning points

  • • Grids for two events
  • • Listing in order
  • • Venn diagrams
  • • Two-way tables

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

enumeratecombinationssystematicallytablesdiagrams

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Listing outcomes with tables and Venn diagrams

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams

2

What you already know

Part 2 of 19

Before we start

What you already know

You can write probabilities and read a two-way table.

Recap: Probabilities that sum to one
3

Key words

Part 3 of 19

Key words

Words you'll need today

sample space
The complete list of possible outcomes.
intersection
Outcomes in both sets — the overlap of a Venn diagram.
union
Outcomes in either set, or both.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Systematic listing

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 19

Learn

Grids for two events

For two dice, a 6 × 6 grid of totals gives all 36 outcomes with none missed. P(total 7) = 6/36 = 1/6. For a coin and a spinner, a grid of rows and columns does the same job. Draw the grid rather than trying to hold the list in your head.

6

Explore the idea

Part 6 of 19

Learn

Listing in order

Without a grid, work in a fixed order. Outfits from 3 tops and 4 trousers: keep the top constant and change the trousers — 3 × 4 = 12. For choosing 2 people from A, B, C, D: AB, AC, AD, BC, BD, CD — six pairs, since AB and BA are the same pair.

7

Quick check

Part 7 of 19

Quick check

How many outcomes when rolling two dice?

8

Quick check

Part 8 of 19

Quick check

P(total of 5) with two dice?

9

Reset break

Part 9 of 19

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — Venn diagrams and tables

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 19

Learn

Venn diagrams

Two overlapping circles split into four regions: only A, only B, both, and neither. Always fill the overlap first. If 18 do maths, 14 do art, 6 do both and 4 do neither, the total is 12 + 6 + 8 + 4 = 30 — note that 18 and 14 already include the 6.

12

Explore the idea

Part 12 of 19

Learn

Two-way tables

Two-way tables cross two categories and include totals in the margins. They are excellent for probability: P(a girl who walks) reads straight from one cell over the grand total. Check every row and column adds to its total before using the table, since one wrong cell corrupts every answer from it.

13

Quick check

Part 13 of 19

Quick check

How many pairs from 5 people?

14

Quick check

Part 14 of 19

Quick check

20 play tennis, 15 swim, 8 do both, 5 do neither. Total?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Counting AB and BA as two different pairs.
  • Putting the 'both' figure only in one circle of a Venn diagram.
  • Forgetting the 'neither' region outside the circles.
16

Challenge round

Part 16 of 19

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Two-way ____ cross two categories and include totals in the margins.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Listing outcomes with tables and Venn diagrams

6 questions, marked with the reasoning shown. No timer.

  1. 1. 4 shirts and 5 ties give how many combinations?

  2. 2. The overlap of a Venn diagram is the...

  3. 3. Fill in a Venn diagram starting with the...

  4. 4. P(double) with two dice?

  5. 5. A complete list of outcomes is called the...

  6. 6. In a two-way table, rows and columns must add to...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 19 · Watch & discover

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