Probability that adds to one
Probability is a measure of expectation on a scale from 0 to 1. The single most useful fact is that the probabilities of all possible outcomes must total exactly 1.
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 total is always 1
- • Complementary events
- • Expected frequency
- • Relative frequency and fairness
This lesson at a glance
- 28 minutes
- 20 parts to scroll through
- 4 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 20
Visual introductionPicture this
Probability that adds to one
Probability is a measure of expectation on a scale from 0 to 1. The single most useful fact is that the probabilities of all possible outcomes must total exactly 1.
In a nutshell
Understand that the probabilities of all possible outcomes sum to 1
Learning cycle
Part 2 of 20
Learning cycle 1 of 2
Part 1 · The total is always 1
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 20
Learn
The total is always 1
If a spinner lands on red with probability 0.3 and blue with 0.45, then green must have probability 1 − 0.3 − 0.45 = 0.25. This 'complete the set' reasoning solves a large share of exam questions with one subtraction.
Reset break
Part 4 of 20
Pause
That's sitting 1 of 5 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 20
Learn
Complementary events
The probability that an event does not happen is 1 minus the probability that it does. If the chance of rain is 0.18, the chance of no rain is 0.82. Recognising a question as a complement is often much faster than adding many separate cases.
Quick check
Part 6 of 20
Quick check
Part 7 of 20
Reset break
Part 8 of 20
Pause
That's sitting 2 of 5 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 20
Learning cycle 2 of 2
Part 2 · Expected frequency
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 20
Learn
Expected frequency
Expected frequency is probability multiplied by the number of trials. With P(six) = 1/6 and 300 rolls, you expect about 50 sixes. 'About' matters: actual results vary, and expected frequency describes a long-run tendency, not a guarantee.
Explore the idea
Part 11 of 20
Learn
Relative frequency and fairness
Relative frequency is the number of successes divided by the number of trials, and it estimates probability better as the number of trials grows. If a die gives 90 sixes in 300 rolls when 50 were expected, that is evidence of bias, though not proof from one experiment alone.
Reset break
Part 12 of 20
Pause
That's sitting 3 of 5 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.
Quick check
Part 13 of 20
Quick check
Part 14 of 20
Explore the idea
Part 15 of 20
Worked example
Worked answer: a spinner has P(red) = 0.3 and P(blue) = 0.45. Find P(green) and the expected greens in 200 spins (3 marks)
All probabilities total 1, so P(green) = 1 − 0.3 − 0.45 = 0.25 (1). Expected frequency = probability × trials = 0.25 × 200 (1) = 50 greens (1). This is an expectation over many spins, so an actual set of 200 spins might give 44 or 57 greens without the spinner being unfair.
Reset break
Part 16 of 20
Pause
That's sitting 4 of 5 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 17 of 20
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 18 of 20
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 19 of 20
Marked quiz
End of lesson quiz: Probability that adds to one
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 20 of 20
Lesson round-up
Ready when you are
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 20 · Watch & discover
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Understand that the probabilities of all possible outcomes sum to 1