Chance Experiments & Variation
Record Your Coin Flips (20 Flips)
Flip a coin 20 times. Record each result in the tally chart.
| Item | Tally | Total |
|---|---|---|
Heads | ||
Tails |
Record Your Coin Flips (30 Flips)
Flip a coin 30 times. Record each result.
| Item | Tally | Total |
|---|---|---|
Heads | ||
Tails |
Expected vs Actual – Coins (Set A)
Think about what you expect and what actually happens.
If you flip a coin 20 times, you expect roughly:
If you got 12 heads and 8 tails, that is:
If you repeat the experiment, will you get exactly the same results?
Expected vs Actual – Coins (Set B)
Circle the correct answer.
Getting 20 heads in a row is:
Getting 11 heads out of 20 flips is:
The more times you flip, the closer to 50/50 you get. This is:
Dice Rolling Experiment (30 Rolls)
Roll a dice 30 times. Record each number.
| Item | Tally | Total |
|---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 |
Dice Rolling Experiment (50 Rolls)
Roll a dice 50 times. Record each number.
| Item | Tally | Total |
|---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 |
Understanding Dice Variation (Set A)
Answer about your dice experiment.
If you roll a dice 30 times, each number should appear about:
Will every number appear exactly 5 times?
If you did the experiment again, the results would be:
Understanding Dice Variation (Set B)
Circle the correct answer.
Rolling a 6 ten times in a row means the dice is:
If you roll 50 times vs 10 times, results will be:
Every roll of a fair dice is:
True or False? (Chance Experiments)
Circle TRUE or FALSE.
More trials give results closer to expected
If you flip 3 heads in a row, tails is 'due'
Variation is natural in chance experiments
A fair dice always gives equal results
Spinner Experiment – 3 Colours (30 Spins)
Spin a 3-colour spinner (equal sections) 30 times. Record each result.
| Item | Tally | Total |
|---|---|---|
Red | ||
Blue | ||
Green |
Spinner Experiment – 4 Colours (40 Spins)
Spin a 4-colour spinner (equal sections) 40 times. Record results.
| Item | Tally | Total |
|---|---|---|
Red | ||
Blue | ||
Green | ||
Yellow |
Expected vs Actual – Spinner (Set A)
A spinner has 3 equal sections. You spin 30 times.
You expect each colour about:
Getting Red 12, Blue 9, Green 9 is:
Getting Red 25, Blue 3, Green 2 would be:
Expected vs Actual – Spinner (Set B)
A spinner has 4 equal sections. You spin 40 times.
You expect each colour about:
Getting 11, 9, 10, 10 is:
If one colour appeared 25 times out of 40, that suggests:
True or False? (Chance Experiments – Set B)
Circle TRUE or FALSE.
If you roll a dice 6 times, each number will appear exactly once
Variation means results differ from trial to trial
More trials make results closer to expected values
If a coin lands on heads 5 times, tails must come next
True or False? (Chance Experiments – Set C)
Circle TRUE or FALSE.
A fair spinner with 4 equal sections gives each section a 1 in 4 chance
Repeating an experiment always gives the same results
If you flip a coin 100 times, results will be closer to 50/50 than with 10 flips
Rolling a dice 12 times guarantees each number appears twice
Match Experiment to Expected Outcome
Draw a line from each experiment to the expected result.
Match Term to Meaning
Draw a line from each term to its definition.
Coin Flip Totals (Set A)
Heads + Tails = Total flips. Find the missing number.
Coin Flip Totals (Set B)
Find the missing number.
Dice Experiment Totals
The 6 dice outcomes must add up to the total rolls. Find the missing number.
Expected or Surprising Results?
Sort each outcome: is it expected or surprising?
More or Fewer Trials?
Sort each statement about trials.
Coin Flip Results – Picture Graph (Set A)
These are results from 20 coin flips. Answer the questions.
| Heads | |
| Tails |
How many more heads than tails?
Is this close to the expected result of 10/10?
Would you say this coin is probably fair? Why?
Coin Flip Results – Picture Graph (Set B)
These are results from 30 coin flips.
| Heads | |
| Tails |
How many total flips?
How close to 15/15 was this result?
Would doing 100 flips likely give a result closer to 50/50?
Dice Rolling Results – Picture Graph
These are results from 30 dice rolls.
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 |
Which number appeared most often?
Which appeared least often?
Each number was expected about 5 times. Were results close?
Does this suggest the dice is fair? Why?
Record and Reflect – Marble Draws
Put 3 red and 2 blue counters in a bag. Draw one, record the colour, replace it. Repeat 20 times.
Red was drawn ___ times. Blue was drawn ___ times.
You expected red about ___ times and blue about ___ times. Were you close?
Why might your results not be exactly 12 red and 8 blue?
Predicting from Experiments (Set A)
Use experimental results to predict.
Spinner has 2 red sections and 1 blue. After 30 spins, you expect red about:
After 60 spins of the same spinner, red should appear about:
You got 22 red out of 30. This is:
Predicting from Experiments (Set B)
Circle the best prediction.
A bag has 1 red and 3 blue. In 20 draws (with replacement), you expect red:
You drew red 7 times out of 20 from a 1-red-3-blue bag. This is:
With more draws, results should get:
Describe Your Coin Flip Results
Write about what happened in your coin flip experiment.
How many heads? How many tails? How close to 10/10?
Was your result exactly what you expected? Why or why not?
If you did it again, would you expect the same result? Explain.
Describe Your Dice Results
Write about your dice experiment.
Which number came up the most? The least?
Were all numbers rolled about the same number of times?
Why do we get different results each time even though the dice is fair?
Compare Two Experiments
Compare results from different experiments.
Compare your 20-flip results with your 30-flip results. Which was closer to 50/50?
Compare your 30-roll results with your 50-roll results. Which was more even?
What does this tell you about the number of trials?
Spinner Experiment Reflection
Make a spinner with 3 equal sections (red, blue, green). Spin 30 times.
Record your results: Red = ___, Blue = ___, Green = ___
Each colour should appear about ___ times. Were your results close?
What if the spinner had 2 sections red and 1 blue? What would you expect?
Unequal Spinner Experiment
Make a spinner with 2 equal red sections and 1 blue section. Spin 30 times.
Record: Red = ___, Blue = ___
You expected red about 20 times and blue about 10 times. How close were you?
Why did red come up more often?
Predicting from Experiments (Set C)
Use experimental data to make predictions.
You flipped 14 heads out of 20. You predict heads is:
You rolled a 6 eight times out of 30. You expect 6 to appear:
A spinner landed on red 18 times out of 30. Red section is probably:
Class Comparison
Answer these questions about comparing experiments.
If every student in your class flipped a coin 20 times, would everyone get the same result?
If you added up ALL the class's heads and tails, would it be close to 50/50? Why?
Class Comparison (Set B)
Answer about comparing class experiments.
If 5 students each roll a dice 30 times, will they all get the same most-common number? Why or why not?
If we combine all 150 rolls (5 × 30), would the results be more even? Why?
What does this tell us about sample size?
Drawing Conclusions from Experiments
Answer each question about experimental results.
You rolled a dice 60 times: 1=9, 2=11, 3=10, 4=10, 5=8, 6=12. Is the dice fair? Why?
A friend got 1=3, 2=2, 3=1, 4=0, 5=2, 6=2 in only 10 rolls. Is the dice fair? Can you tell from 10 rolls?
Match Experiment to Conclusion
Draw a line from each experiment to its best conclusion.
Design Your Own Experiment
Design a chance experiment.
What will you test? (coin, dice, spinner, cards?)
How many trials will you do?
What do you predict will happen?
Record your results:
Were your results close to your prediction? Describe the variation.
Challenge: Fair or Unfair?
Think about fairness in chance experiments.
You roll a dice 60 times and get: 1 = 8, 2 = 11, 3 = 10, 4 = 9, 5 = 12, 6 = 10. Is the dice fair? Explain.
How many times would you need to roll to be more confident about whether it is fair?
How could you test if a coin is fair?
Home Activity: More Chance Experiments
Try more chance experiments at home!
- 1Spin a spinner (or make one from a paper plate) 30 times. Record and compare to expected.
- 2Put 3 red and 2 blue counters in a bag. Draw one 20 times (replace each time). Is red picked more?
- 3Flip 2 coins at once, 20 times. How often do you get 2 heads? Is it what you expected?
- 4Compare your results with a family member. Did you get the same? Discuss why or why not.
Dice Roll Experiment (60 Rolls)
Roll a dice 60 times and tally the results.
| Item | Tally | Total |
|---|---|---|
Rolled a 1 | ||
Rolled a 2 | ||
Rolled a 3 | ||
Rolled a 4 | ||
Rolled a 5 | ||
Rolled a 6 |
Experimental vs Theoretical Probability
Compare what you expect to what actually happens.
Theoretical probability of each number on a dice = ___. For 60 rolls, expected frequency of each = ___
Look at a set of 60 dice rolls. Were any numbers very different from expected? Which ones?
If you rolled 600 times instead of 60, would you expect the results to be closer to theoretical? Why?
Variation in Chance Experiments (Set A)
Circle the correct answer.
You flip a coin 10 times and get 8 heads. This means:
You repeat an experiment and get different results. This is called:
To get results closer to theoretical probability, you should:
Experimental probability of heads after 100 flips: 53 heads. This is:
Planning a Chance Experiment
Plan a complete chance experiment.
What will I test? (coin, dice, spinner, cards?)
How many trials will I do?
What is the theoretical probability of my target outcome?
What do I predict will happen?
Record and Analyse Experiment Results
Record the results of your experiment and compare to predictions.
Record your results (tally or list):
Experimental probability of your target outcome = ___/___
Theoretical probability = ___. Are they close?
Describe the variation in your results.
Spinner Results (Scale: 1 icon = 2 spins)
A spinner has 3 equal sections: Red, Blue, Green. After 60 spins:
| Red | |
| Blue | |
| Green |
How many times did each colour appear?
Theoretical probability of each colour = 1/3. Expected frequency for 60 spins = ___
Which result was furthest from the expected frequency?
Would repeating the experiment 600 times give results closer to 1/3 each?
Simulating Real Events
Use a chance experiment to simulate a real situation.
A weather forecast says there is a 50% chance of rain each day this week. Use a coin flip to simulate rain (heads = rain). Flip the coin 7 times. Record results.
On how many simulated days did it rain?
Run the simulation 3 times. Do you always get the same answer? What does this tell you?
Analysing a Long-Run Frequency
Investigate how results change as the number of trials increases.
Flip a coin 10 times. Record proportion of heads: ___/10 = ___
Flip it another 10 times (total 20). New proportion: ___/20 = ___
Flip 30 more (total 50). Proportion: ___/50 = ___
What do you notice about the proportion as trials increase?
Sort: Natural Variation or Unfair Device?
Decide if each result is likely to be natural variation or evidence of an unfair device.
Compare Two Experiments
Two students run the same coin-flip experiment.
Student A: 20 flips, 13 heads. Student B: 20 flips, 9 heads. Are these results surprising? Why?
If they combined results: 22 heads in 40 flips. Proportion = ___. Is this closer to 1/2?
Why do two students doing the same experiment get different results?
Challenge: Is This Dice Fair?
Analyse this dice roll data to determine if the dice is fair.
Results from 120 rolls: 1=18, 2=20, 3=19, 4=22, 5=21, 6=20. Expected frequency of each number = ___. Are these results within normal variation?
Now consider: 1=5, 2=7, 3=6, 4=8, 5=89, 6=5. Is this dice likely fair? Explain.
How many trials would you need to be more confident that a dice is fair?
Probability Summary and Reflection
Reflect on everything you have learned about probability.
Write three things you know about probability and chance experiments.
What is the most important thing to remember about the difference between theoretical and experimental probability?
Give a real-life situation where understanding probability would be helpful.