GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7
CHANCE — Uncertainty and random experiments
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own prediction.
You know the two faces of a coin. Does knowing the possible results tell you which will appear next?
Write or sketch a first attempt. Use the model to test your assumptions before accepting a rule.
Understand
A random experiment has identifiable possible outcomes, but its next result is uncertain under the model. A probability describes likelihood, not a promise about a single trial.
Key Ideas
Two possible outcomes alone do not make them equally likely. A car starting and not starting need not have equal chances.
Visualise
Predict one trial
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
Describe the experiment and what is recorded. List possible results. State assumptions such as a fair coin, random toss and independent repeats before assigning probabilities.
Worked Example
Given
One random toss of a fair coin; record H or T.
To Find
Possible outcomes and the probability of heads
Reasoning
Model: S = {H, T}; the two elementary outcomes are equally likely.
Solution
- Favourable outcomes for heads: {H}.
- Probability calculation: 1 favourable outcome out of 2 gives .
Result
P(H) = ; the next outcome is still uncertain.
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 cup may land on its base, rim or side. Is each position automatically assigned 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 155