GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7
OBSERVE — Experimental probability and relative frequency
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own prediction.
A die lands on 4 eight times in 50 rolls. What does the record tell you—and what does it not guarantee?
Write or sketch a first attempt. Use the model to test your assumptions before accepting a rule.
Understand
Experimental probability is the observed event count divided by the positive number of trials. It reports this record; different records can give different proportions.
Key Ideas
Use a positive trial count. This is an observed ratio.
An observed frequency is not a guarantee about the next trial or evidence that the exact model probability equals that frequency.
Visualise
Record, count, compare
Local seeded simulation of independent fair coin tosses. These are generated observations, not textbook experimental data. A fixed seed reproduces the same sequence.
Trials: 0 · Heads: 0 · Tails: 0
No trials yet: observed relative frequency is not defined.
Last 0 results: None yet
Long-run relative frequency tends towards the model value; exact equality at a set number of trials is not guaranteed.
Method
Record every trial consistently. Count occurrences of the specified event, divide by the number of trials and label the answer experimental. With zero trials the ratio is not yet defined.
Worked Example
Given
A 4 is recorded in 8 of 50 die rolls (Example 2).
To Find
Experimental probability of rolling a 4
Reasoning
Observed relative frequency = event count ÷ trial count.
Solution
- Event count is 8; total trials are 50.
- = = 0.16 = 16%.
Result
Experimental probability is 0.16 for this record.
AIMS Method
- A — Attempt independently
Predict and describe what is being recorded. - I — Investigate the idea
Identify the model, evidence and assumptions. - M — Make connections
Connect outcomes, events, fractions and tree paths. - S — Scrutinise your reasoning
Check completeness, likelihoods and changing conditions.
Think first. Use AI purposefully. Verify always.
Focused Practice
A 3 occurs three times in twelve rolls. Calculate the experimental probability.
Check & Feedback
Explain the model, state an assumption and identify one conclusion the information does not justify.
Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 7 · printed page 160