Probability: The Complete Grade 8–9 Guide

Every probability question in the Grade 8–9 syllabus — single events, the complement (not happening), relative frequency, and simple two-event experiments — each worked in full, with a worksheet.

Probability tells you how likely an event is, on a scale from 0 (impossible) to 1 (certain). When all outcomes are equally likely, it's a simple fraction. This guide covers every probability question type in the Grade 8–9 syllabus.

P(event) = number of favourable outcomestotal number of outcomes

1Type 1: Probability of a single event

Worked ExampleExample 1: rolling an even number on a die

1
Sample space (all outcomes): 1, 2, 3, 4, 5, 6 — six in total.
List everything that can happen.
2
Favourable (even) outcomes: 2, 4, 6 — that's 3.
Count only what the event asks for.
3
P(even) = 3⁄6 = 12.
Favourable over total, then simplify.

Worked ExampleExample 2: a bag has 4 red, 3 blue and 5 green balls. P(green)?

1
Total balls = 4 + 3 + 5 = 12.
The total number of outcomes.
2
Favourable (green) = 5.
Count the greens.
3
P(green) = 5⁄12.
Won't simplify further.

2Type 2: The complement (event NOT happening)

The probability an event does not happen is 1 minus the probability it does. All probabilities for an experiment add up to 1.

Worked ExampleExample 3: if P(rain) = 0,3, find P(no rain)

1
P(no rain) = 1 − P(rain).
The two possibilities must total 1.
2
= 1 − 0,3 = 0,7.

Worked ExampleExample 4: P(not drawing a red) from 4 red in 12 balls

1
P(red) = 4⁄12 = 13.
First find the event itself.
2
P(not red) = 1 − 13 = 23.
Complement rule.

3Type 3: Relative frequency (experimental probability)

Relative frequency is what actually happened: number of successes ÷ number of trials. With many trials it gets close to the theoretical probability.

Worked ExampleExample 5: a coin lands heads 27 times in 50 tosses

1
Relative frequency of heads = 27⁄50 = 0,54.
Successes over trials.
2
Theoretical probability is 0,5, so the experiment is close.
More tosses would usually bring it nearer to 0,5.

4Type 4: Two-event experiments (list the outcomes)

A tree diagram for tossing two coins: the four equally likely outcomes are HH, HT, TH and TT.

Worked ExampleExample 6: tossing two coins: P(two heads)?

1
List all outcomes: HH, HT, TH, TT — four in total.
Each coin is independent, giving 2 × 2 = 4 combinations.
2
Favourable (two heads): only HH — that's 1.
Count the matching outcome(s).
3
P(two heads) = 1⁄4.
Favourable over total.

💡

Probability can be written as a fraction, a decimal or a percentage — 12 = 0,5 = 50%. Give whichever the question asks for.

⚠️

A probability is never more than 1 or less than 0. If you get an answer like 3⁄2, you've miscounted the outcomes or the total.

Probability grows into Venn diagrams and tree diagrams in Grade 10–12, so these foundations matter. Work through every type in the worksheet.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
A bag has 3 red and 5 blue balls. P(red)? (single)
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3⁄8
2
P(rolling a number greater than 4 on a die)? (single)
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5, 6 → 2⁄6 = 13
3
A bag has 2 red, 3 blue, 5 yellow. P(yellow)? (single)
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5⁄10 = 12
4
If P(win) = 0,35, find P(not win). (complement)
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1 − 0,35 = 0,65
5
P(not rolling a 6 on a die)? (complement)
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1 − 1⁄6 = 5⁄6
6
A spinner is 4 equal colours. P(not green)? (complement)
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1 − 14 = 34
7
A die is rolled 60 times; a 3 comes up 12 times. Relative frequency? (rel. freq.)
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12⁄60 = 0,2
8
Two coins are tossed. P(one head and one tail)? (two events)
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HT or TH → 2⁄4 = 12
9
Two coins are tossed. P(no heads)? (two events)
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Only TT → 14
10
P(drawing a vowel) from the letters of MATHS? (single)
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Only A → 1⁄5