← Investigators MathsProbability and chance30 minutesStd 6–8

Is the Die Fair

✨ Twenty rolls look wildly uneven, but at 120 rolls the six bars have quietly flattened out.

Two bar charts of the same die: after twenty rolls the six bars are very uneven against an expected line of 3.3, and after one hundred and twenty rolls they are nearly level with the expected line of twenty. — How it works

🧰 You need

one die
a cup to shake it in
paper and pencil for a tally chart
a calculator
squared paper

👀 What you will see

After 20 rolls some faces may appear five times and others once. After 120 rolls the bars are far more even, though still not identical. No face is perfectly on 20, and that is expected.

🧪 Do it

Write down what you expect the six counts to be after 120 rolls.
Roll the die 20 times, tallying each face, and draw a quick bar chart.
Continue to a total of 120 rolls, keeping the tally going.
Work out the expected count for each face by dividing 120 by 6.
Draw the final bar chart with the expected value marked as a horizontal line.
Write one sentence on how far your biggest and smallest bars are from the expected line.

💡 Why it happens

Each face of a fair die has a probability of one in six, because there are six equally likely outcomes. With only a few trials, random variation makes the results look lumpy, and that lumpiness is normal rather than evidence of a loaded die. As the number of trials grows, the fraction of rolls showing each face gets closer to one sixth, a result called the law of large numbers. This is why testing a claim needs a large sample, whether you are checking a die or a medicine.

🔁 Now try this

Roll two dice 120 times, tally the totals from 2 to 12, and explain why 7 wins so clearly.

🤔 Think about it

After four sixes in a row, is the next roll any less likely to be a six?

🧘 Ask the Acharya

“After four sixes in a row, is the next roll any less likely to be a six?” — ask him and he will explain it from your own chapters.

Ask Guru →

More for Std 6–8

Science25 min