Probability

Fair chance and relative frequency

P(event) = favourable / possible. Relative frequency from a table of trials.

CAPS

Grade 10 · Mathematical Literacy · Probability

Mathematical Literacy uses a context, not a bare sum.

Two papers
Paper 1 uses familiar contexts: pay slips, till slips, maps you have seen, and data in a table. Paper 2 uses less familiar contexts and expects you to decide which method fits. Both papers are 150 marks.
What to show
Write the value with its unit or its rand sign. Say whether you multiply or divide, and round only at the end, in the way the question asked (nearest rand, one decimal place, a whole number of tiles).
The relation
P(E) = n(E)n(S). Theoretical probability
How a marker reads it
Leave probability as a fraction unless they ask for a decimal or percent.

A correct number with the wrong unit, or a VAT amount treated as the full price, loses the mark the context was testing.

Diagram

Worked example

A bag has 3 red and 7 blue marbles. One is drawn at random. P(red)?

Before any working — hunt first

Given

Numbers and units already in the sentence: 3 red · 7 blue. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(red). Circle that word — that is the missing variable.

Find

We are required to find: P(red). Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write P(E) = n(E)n(S) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(red).

Simplified approach

Red marbles over all marbles.

Culture note

A marble game behind the toilets at break is the CAPS bag.

Formulas

P(E)=n(E)n(S)

Theoretical probability

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

If the price already includes VAT, divide by 1.15 — do not subtract 15%
How:Total = price × 1.15 when VAT is still to be added. When the till already shows VAT, price excluding = total1.15. Subtracting 15% of the total is a different number and loses the mark.
When to use it:Till slips, VAT, and SARS-style tax questions.
Fencing is perimeter. Grass, paint and tiles are area. Tanks are volume.
How:Underline the object: wire, border, fence → add the sides. Floor, wall, field, paint → multiply length by width, then divide by coverage and round tins up. Water in a tank → m³ then × 1 000 for litres.
When to use it:Measurement papers: school fields, paint, Jojo tanks.

Step 1 / 5

Count the bag

3 red, 10 in total.

P=310

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

Find the probability that a fair die shows a 6. Write the answer as a simplified fraction.

4. Step-by-step working

01
Write the formula
P=16.
16
02
Divide
Divide top and bottom by 1.
16

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Find the probability that a fair die shows a 6. Write the answer as a simplified fraction.

In other words — as if you have never seen this before

If you have never seen this before: Probability is favourable over possible. Simplify the fraction by dividing the top and the bottom by the same number. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

1 favourable outcomes, 6 equally likely outcomes.

3. Which method — and why this one?

Probability is favourable over possible. Simplify the fraction by dividing the top and the bottom by the same number.

4. Step-by-step working

01 / 05
Write the formula
P=16.
16
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Divide
Divide top and bottom by 1.
16
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Sense-check
A probability is between 0 and 1. More favourable outcomes means a larger fraction.
16
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
04 / 05
Step F — Box the answer with its unit
16
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

Copy onto your answer sheet — in this order

Formula: 16

Answer: 16

6. Check it like a marker

The number of outcomes that do not happen is not the top of the fraction, unless the question asks for the complement.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

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