The probability scale and summing to 1
Every outcome that could possibly happen, added together, always gives exactly 1 — that single fact is a powerful checking tool.
Part of your national curriculum
- Probability: Understand that the probabilities of all possible outcomes sum to 1
Lesson overview
What you'll learn in this lesson
Understand that the probabilities of all possible outcomes sum to 1
Key learning points
- • The scale
- • Worked example
- • Using complements
This lesson at a glance
- 20 minutes
- 17 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 17
Visual introductionPicture this
The probability scale and summing to 1
Every outcome that could possibly happen, added together, always gives exactly 1 — that single fact is a powerful checking tool.
In a nutshell
Understand that the probabilities of all possible outcomes sum to 1
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · The scale
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
The scale
Probability is measured from 0 (impossible) to 1 (certain). All the probabilities of every possible outcome in a situation must add up to exactly 1.
Reset break
Part 4 of 17
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 17
Learn
Worked example
A bag has red, blue and green counters. P(red) = 0.3, P(blue) = 0.45. Since all probabilities sum to 1: P(green) = 1 - 0.3 - 0.45 = 0.25.
Quick check
Part 6 of 17
Quick check
P(red) = 0.3 and P(blue) = 0.45 in a bag with only red, blue and green. What is P(green)?
Quick check
Part 7 of 17
Reset break
Part 8 of 17
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 17
Learning cycle 2 of 2
Part 2 · Using complements
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Using complements
If P(rain tomorrow) = 0.2, then P(no rain) = 1 - 0.2 = 0.8, because 'rain' and 'no rain' are the only two possible outcomes.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
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 17
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 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
All the ____ of every possible outcome in a situation must add up to exactly 1.
If P(rain tomorrow) = 0.2, then P(no rain) = 1 - 0.2 = 0.8, because 'rain' and 'no rain' are the only two ____ outcomes.
Challenge round
Part 15 of 17
Game · Recall cards
P(red) = 0.3 and P(blue) = 0.45 in a bag with only red, blue and green. What is P(green)?
Card 1 of 4
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: The probability scale and summing to 1
4 questions, marked with the reasoning shown. No timer.
1. P(red) = 0.3 and P(blue) = 0.45 in a bag with only red, blue and green. What is P(green)?
2. If P(rain) = 0.2, what is P(no rain)?
3. What must the probabilities of all possible outcomes sum to?
4. P(red) = 0.3, P(blue) = 0.45. P(green) is
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
Quiz score
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Games
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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 LunaPart 1 of 17 · Watch & discover
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Understand that the probabilities of all possible outcomes sum to 1