GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7

EXPECT — Theoretical probability and equal likelihood

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with your own prediction.

There are two Bs in PROBABILITY. Do repeated letters disappear when you count equally selectable letter cards?

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

Understand

For a finite model with equally likely elementary outcomes, P(E) = n $\frac{(E)}{n}$ (S). The elementary outcomes must retain distinctions that make selection equally likely, such as separately labelled cards.

Key Ideas

P (E) = \frac{n (E)}{n (S)}

The colour outcomes {red, blue} are not equally likely when there are 3 red and 7 blue equally selectable marbles.

Visualise

Select an event

Event for a fair die

12 ✓34 ✓56 ✓

S = {1,2,3,4,5,6}. E = {2, 4, 6}. A check mark identifies each favourable outcome.

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

This counting rule applies because the six faces are equally likely. A biased die requires its outcome probabilities instead.

Method

Choose an elementary sample space. Justify equal likelihood. Identify the event, count its outcomes, divide by n(S) and simplify. If outcomes have unequal probabilities, count alone is insufficient.

Worked Example

Given

Eleven equally selectable cards carry the letters of PROBABILITY (Example 4).

To Find

Probability of selecting a B card

Reasoning

Sample-space model: the eleven card positions, including both separate B cards.

Solution

The B cards are positions 4 and 6; n(E) = 2.
There are 11 cards; n(S) = 11.
P(B) = $\frac{2}{11}$ ≈ 0.182.

Result

P(B) = $\frac{2}{11}$ , approximately 18.2%.

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. Find the probability of an even result and explain the equal-likelihood assumption.

Your reasoning

Continue with THEORETICAL →

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 161