--- title: "Simple Chance Experiments" description: "Repeat fair coin flips, fair six-sided die rolls and counter draws. Record every result and compare the counts with predictions based on the chances. Put each counter back and mix before the next draw" canonical: https://lightmysky.com/learn/mathematics/simple-chance-experiments-mt_J4j7d3iAfg source: https://lightmysky.com/learn/mathematics/simple-chance-experiments-mt_J4j7d3iAfg.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Simple Chance Experiments Repeat fair coin flips, fair six-sided die rolls and counter draws. Record every result and compare the counts with predictions based on the chances. Put each counter back and mix before the next draw. Subject: Mathematics · Area: Probability · Ages 9 to 10 Page: https://lightmysky.com/learn/mathematics/simple-chance-experiments-mt_J4j7d3iAfg ## Ready when they can - Predict about 10 heads in 20 fair coin flips, tally heads and tails, and compare the recorded counts with the prediction - Roll a fair six-sided die 30 times, record every result, and compare each number's count with the expected count of about 5 - Draw same-size, same-shape counters from a mixed bag without looking or choosing by feel, record and replace each counter, and compare the results with a prediction ## Lesson: Doing a chance experiment You know words like likely and unlikely. A chance experiment repeats an action with an uncertain result. Choose how many trials to make. Record each result once with a tally mark. The fifth tally crosses the first four. Add the counts to check that every trial was recorded. On a bar chart, read each bar's name and printed number to find its count. When a coin lands flat, record heads or tails. A fair coin gives both sides an equal chance, so expect about half the flips to be heads and half tails. Find an expected count by dividing the number of flips by 2. Find a missing tails count by subtracting heads from the total. A prediction says what you expect. A recorded count says what happened. *(drawing: Maya expected about 8 of each in 16 fair coin flips. She recorded 9 heads and 7 tails. Her counts add to 16.)* A fair six-sided die has numbers 1 to 6, each with the same chance on every roll. Make a tally column for each number. Divide the total rolls by 6 to find each expected count. For 36 rolls, 36 divided by 6 is 6, so expect about 6 of each. Recorded counts may be higher or lower. Later rolls do not have to balance earlier counts. One count matching its prediction does not prove the die is fair. *(drawing: Ben expected about 6 of each number. His recorded counts add to 36, but they are not all equal.)* For a bag experiment, use counters of the same size and shape. Mix before each draw. Take one without looking or choosing by feel. Record its colour, put it back, and mix again. Putting it back keeps the bag's contents unchanged. With equal numbers of red and blue counters, each colour has an even chance. Expect about half the draws to be red. In 18 draws, half is 9. **Example.** With equal chances for red and blue, expect half the draws to be red. In 18 draws, Ada expects 9 red but records 11 red and 7 blue. Subtract expected from recorded: 11 - 9 = 2 more red than expected. To compare the recorded colours, subtract the smaller count from the larger. To combine batches, add each colour's counts across batches. A fair coin can give a short streak, such as all heads. A streak alone does not prove fairness or unfairness. More trials give more evidence. In larger fair experiments, the shares of outcomes usually get closer to their chances. They need not match exactly, and each extra trial need not bring them closer. **Example.** Compare shares when experiments have different totals. One group records 24 heads in 40 flips. Another records 48 heads in 80 flips. Both the total and the heads count doubled, so the heads share is the same. The larger experiment is not closer to half in this example. **Recap.** A chance experiment lets you test what you expect against what really happens. *Lesson, questions and flashcards written for this dataset.* ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Likelihood Language](https://lightmysky.com/learn/mathematics/likelihood-language-mt_iFFKZd-Vgv) ## Optional connections - [Pictograms and tally charts](https://lightmysky.com/learn/mathematics/pictograms-and-tally-charts-mt_c29FaCTNsx) ## Opens up - [Experimental vs Theoretical](https://lightmysky.com/learn/mathematics/experimental-vs-theoretical-mt_-bMnJcPJy8) - [Probability as a Fraction](https://lightmysky.com/learn/mathematics/probability-as-a-fraction-mt_-c4Ca_nBzX)