Good Learning Co.
SavannahYear 8
← Maths
MathsProbability25 min★★ difficulty

Listing outcomes with tables and Venn diagrams

Trying to list outcomes randomly means you'll miss some — a table or grid forces you to be systematic so nothing slips through.

Part of your national curriculum
  • Probability: Enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams

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

  • • Sample space diagrams
  • • Worked example
  • • Venn diagrams

This lesson at a glance

  • 25 minutes
  • 13 parts to scroll through
  • 3 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 13 · Discover8%
1

Watch & discover

Part 1 of 13

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

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Sample space diagrams

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

3

Explore the idea

Part 3 of 13

Learn

Sample space diagrams

Rolling two dice has 6 × 6 = 36 equally likely outcomes, best shown in a grid with one die's results along the top and the other down the side.

4

Explore the idea

Part 4 of 13

Learn

Worked example

Using the dice grid, count outcomes that total 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 outcomes out of 36, so P(sum = 7) = 6/36 = 1/6.

5

Quick check

Part 5 of 13

Quick check

Rolling two fair dice, how many equally likely outcomes are there in total?

6

Reset break

Part 6 of 13

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
7

Quick check

Part 7 of 13

Quick check

How many of those 36 outcomes give a sum of 7?

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Venn diagrams

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

9

Explore the idea

Part 9 of 13

Learn

Venn diagrams

In a class of 30, 18 like football and 12 like tennis, with 5 liking both. A Venn diagram shows 5 in the overlap, 13 football-only, 7 tennis-only, and 30-18-12+5=5 liking neither.

10

Quick check

Part 10 of 13

Quick check

In a Venn diagram, where do items that satisfy both conditions go?

11

Challenge round

Part 11 of 13

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

12

Mastery quiz

Part 12 of 13

Marked quiz

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

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

  1. 1. Rolling two fair dice, how many equally likely outcomes are there in total?

  2. 2. How many of those 36 outcomes give a sum of 7?

  3. 3. In a Venn diagram, where do items that satisfy both conditions go?

13

Lesson round-up

Part 13 of 13

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 3 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 13 · Watch & discover

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

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