GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7

SCALE — Probability from 0 to 1

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with your own prediction.

From six equally selectable cards, none, three or all six are purple. Where would each chance lie on a number line?

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

Understand

Probability lies from 0 to 1. In these finite models, 0 is impossible and 1 is certain. At $\frac{1}{2}$ an event and its complement have equal chances. The complement contains all outcomes outside the event.

Key Ideas

0 \leq P (E) \leq 1

P (E) + P (not E) = 1

If a match can be drawn, P(win) = $\frac{1}{2}$ means P(not win) = $\frac{1}{2}$ ; it does not by itself mean P(lose) = $\frac{1}{2}$ .

Visualise

Locate the chance

Purple cards out of six: 3

PPPGGG

0
Impossible

\frac{1}{2}

Even chance1
Certain

P (purple) = \frac{3}{6}

Even chance of purple versus not purple. Each card is equally selectable. The complementary event has 3 favourable cards.

Method

Name the event and its complement. Locate the probability between 0 and 1. Use P(not E) = 1 − P(E). A decimal can also be written as a fraction or percentage.

Worked Example

Given

Six equally selectable cards; three purple and three green.

To Find

Probability of drawing purple and probability of not drawing purple

Reasoning

The event and its complement partition all six cards.

Solution

P(purple) = $\frac{3}{6}$ = $\frac{1}{2}$ .
P(not purple) = 1 − $\frac{1}{2}$ = $\frac{1}{2}$ .

Result

An even chance of purple versus not purple.

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 fair die is rolled. Give one impossible event and one certain event.

Your reasoning

Continue with CHANCE & SCALE →

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 157