MathsProbability23 min★ difficulty

Experimental probability from real trials

Roll a die 60 times and the results almost never split perfectly evenly — experimental probability is about what actually happens, not just what should.

Part of your national curriculum

Probability: Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes

Lesson overview

What you'll learn in this lesson

Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes

Key learning points

• Relative frequency
• Worked example
• Fair vs unequally likely

This lesson at a glance

23 minutes
14 parts to scroll through
3 quick checks
Marked quiz at the end
Gentle pace: short sittings with pauses

Words to know

recordfrequencyoutcomessimpleprobability

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%

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Part 1 of 14

Watch first

Experimental probability from real trials

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

In a nutshell

Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Relative frequency

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

Explore the idea

Part 3 of 14

Learn

Relative frequency

Experimental (or relative) probability = number of successful trials ÷ total number of trials. The more trials you run, the closer this usually gets to the true probability.

Explore the idea

Part 4 of 14

Learn

Worked example

A coin is flipped 40 times and lands heads 18 times. The experimental probability of heads = 18/40 = 0.45, compared with the theoretical 0.5.

Quick check

Part 5 of 14

Quick check

A coin is flipped 40 times, landing heads 18 times. What is the experimental probability of heads?

Reset break

Part 6 of 14

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

Quick check

Part 7 of 14

Quick check

What happens to experimental probability as more trials are run?

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Fair vs unequally likely

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

Explore the idea

Part 9 of 14

Learn

Fair vs unequally likely

A fair die gives each of its six outcomes equal probability, 1/6 each. A biased spinner might give unequal probabilities, e.g. red twice as likely as blue, which experiments can reveal by counting frequencies.

Quick check

Part 10 of 14

Quick check

What is true of a fair six-sided die?

Challenge round

Part 11 of 14

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 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Experimental (or relative) ____ = number of successful trials ÷ total number of trials.

A fair die gives each of its six ____ equal probability, 1/6 each.

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Experimental probability from real trials

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

1. A coin is flipped 40 times, landing heads 18 times. What is the experimental probability of heads?
2. What happens to experimental probability as more trials are run?
3. What is true of a fair six-sided die?

Lesson round-up

Part 14 of 14

Lesson round-up

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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

Work out the total cost of the trip if 50 pupils go.
Show why the price per pupil falls when more pupils go, using numbers.
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

Write your answer, notes or working here

Saved as you type.

Photos of paper work, diagrams or working outHow many minutes did the written work take?

Part 1 of 14 · Watch & discover

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Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes