---
title: "Experimental probability"
description: "Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability"
canonical: https://lightmysky.com/learn/mathematics/experimental-probability-mt_sHJqh6UUya
source: https://lightmysky.com/learn/mathematics/experimental-probability-mt_sHJqh6UUya.md
retrieved: 2026-10-19
---

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# Experimental probability

Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

Subject: Mathematics · Area: Probability · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/experimental-probability-mt_sHJqh6UUya

## Ready when they can

- Conduct a coin-toss experiment, record results in a frequency table, and calculate relative frequencies
- Compare experimental results with theoretical probability and explain discrepancies
- Explain that for independent trials with a fixed outcome probability, larger samples usually give relative frequencies nearer that probability, without guaranteeing a closer result in any particular run.

## Lesson: Relative frequency: what really happened

Relative frequency describes observed results: the number of times an outcome occurred divided by the total number of trials. Use your own data or results someone else recorded. Write the share as a fraction, or do the division to get a decimal.

*(drawing: Priya tossed a fair coin 20 times and got 12 heads and 8 tails.)*

**Example.** Priya uses a fair coin, so the theoretical probability of heads is 0.5. Her 12 heads in 20 tosses give 12 ÷ 20 = 0.6. To compare with theory, find the gap: 0.6 minus 0.5 is 0.1. A short run can differ from theory just by chance. An exact match can also happen; neither result proves fairness.

*(drawing: Priya tossed the same coin 200 times and got 99 heads and 101 tails. The relative frequency of heads, 99 ÷ 200 = 0.495, sits much closer to 0.5.)*

In independent trials, knowing one result does not change the chance of another. If the chance stays the same, larger samples usually give a relative frequency nearer that chance. A particular longer run can still be farther away.

To combine runs under the same conditions, add their outcome counts and add their trial counts. Divide the combined outcome count by the combined trial count.

**Recap.** Relative frequency is outcome count divided by trials. With independent trials and a fixed chance, more trials usually give a closer estimate, without a guarantee.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [Experimental vs Theoretical](https://lightmysky.com/learn/mathematics/experimental-vs-theoretical-mt_-bMnJcPJy8)
- [The Probability Scale](https://lightmysky.com/learn/mathematics/the-probability-scale-mt_vmQJAtAFuy)

## Opens up

- [Tree diagrams](https://lightmysky.com/learn/mathematics/tree-diagrams-mt_GDtFU5fyUv)
- [Relative Frequency and Expected Outcomes](https://lightmysky.com/learn/mathematics/relative-frequency-and-expected-outcomes-mt_OQCnzkcHUH)
- [Risk, Insurance and Pooling](https://lightmysky.com/learn/civics-and-economics/risk-insurance-and-pooling-mt_zrMeXUHV4Y)