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
- 16 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 16
Visual introductionPicture this
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.
In a nutshell
Enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams
Learning cycle
Part 2 of 16
Learning cycle 1 of 2
Part 1 · Sample space diagrams
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 16
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.
Reset break
Part 4 of 16
Pause
That's sitting 1 of 4 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.
Explore the idea
Part 5 of 16
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.
Quick check
Part 6 of 16
Quick check
Rolling two fair dice, how many equally likely outcomes are there in total?
Quick check
Part 7 of 16
Reset break
Part 8 of 16
Pause
That's sitting 2 of 4 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.
Learning cycle
Part 9 of 16
Learning cycle 2 of 2
Part 2 · Venn diagrams
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 16
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.
Quick check
Part 11 of 16
Reset break
Part 12 of 16
Pause
That's sitting 3 of 4 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.
Challenge round
Part 13 of 16
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
Challenge round
Part 14 of 16
Game · Recall cards
Rolling two fair dice, how many equally likely outcomes are there in total?
Card 1 of 4
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Listing outcomes with tables and Venn diagrams
4 questions, marked with the reasoning shown. No timer.
1. Rolling two fair dice, how many equally likely outcomes are there in total?
2. How many of those 36 outcomes give a sum of 7?
3. In a Venn diagram, where do items that satisfy both conditions go?
4. Rolling two dice, P(total 7) is
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
Quiz score
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Points this lesson
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Best run
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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 16 · Watch & discover
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Enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams