GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7

SPACE — Sample spaces, n(S) and events

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with your own prediction.

When two coins are distinguished by first and second, are HT and TH the same outcome?

Write or sketch a first attempt. Use the model to test your assumptions before accepting a rule.

Understand

S contains all possible recorded outcomes, without duplicates. n(S) counts its elements. An event E is a subset of S. Choose enough detail for the question; grouped outcomes need not be equally likely.

Key Ideas

S = {HH, HT, TH, TT}

Recording only the number of heads gives {0,1,2}, but these values are not equally likely for two independent fair tosses.

Visualise

Build a complete sample space

Recorded experiment

HHHTTHTT

n(S) = 4. Every possible recorded outcome appears once.

Uniform probabilities require fair independent coin tosses and, for cards, uniform independent selection.

Method

Specify what is recorded and how order is distinguished. Enumerate systematically. Check completeness and uniqueness, then select the outcomes satisfying the event.

Worked Example

Given

Two independent fair coin tosses; record the ordered results.

To Find

Probability of at least one head

Reasoning

S = {HH, HT, TH, TT}; each ordered outcome has probability $\frac{1}{4}$ .

Solution

Favourable event E = {HH, HT, TH}.
n(E) = 3; n(S) = 4.
P(E) = $\frac{3}{4}$ .

Result

At least one head has probability $\frac{3}{4}$ .

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

For a coin and a numbered card from 1 to 6, how many ordered outcomes are there?

Your reasoning

Continue with SAMPLE SPACE & EVENTS →

Check & Feedback

Explain the model, state an assumption and identify one conclusion the information does not justify.

Explain your conclusion

Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 7 · printed page 166