Probability — Grade 8 & 9 Maths (CAPS)

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

Also known as: chance · likelihood · probability of an event

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 the probability question types of Grade 8 and 9.

When every outcome is equally likely: P(event) = (number of favourable outcomes)/(total 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 = 1/2.
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. The probabilities of all the possible outcomes of 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 = 1/3.
First find the event itself.
2
P(not red) = 1 − 1/3 = 2/3.
Complement rule.

3Type 3: Relative frequency (experimental probability)

Relative frequency is what actually happened: number of successes ÷ number of trials. With many trials it usually settles 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 (tree diagrams and two-way tables)

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 toss has 2 possible outcomes, so two tosses give 2 × 2 = 4 possible ordered outcomes.
2
Favourable (two heads): only HH — that's 1.
Count the matching outcome(s).
3
P(two heads) = 1/4.
Favourable over total.

A two-way table lists every outcome of two events at once: one event along the top, the other down the side, and each cell is one outcome. For a coin and a die:

	1	2	3	4	5	6
H	H1	H2	H3	H4	H5	H6
T	T1	T2	T3	T4	T5	T6

Worked ExampleExample 7: a coin is tossed and a die is rolled. Use the two-way table to find P(a head and an even number)

1
The table has 2 rows and 6 columns: 2 × 6 = 12 equally likely outcomes.
Each cell is one outcome, so count the cells.
2
A head and an even number: H2, H4 and H6 — 3 cells.
Read along the H row and pick the even columns.
3
P(head and even) = 3/12 = 1/4.
Favourable over total, simplified.

💡

Probability can be written as a fraction, a decimal or a percentage — 1/2 = 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.

Tree diagrams and two-way tables are Grade 9 tools; Venn diagrams and contingency tables follow 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 = 1/3
3
A bag has 2 red, 3 blue, 5 yellow. P(yellow)? (single)
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5/10 = 1/2
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 − 1/4 = 3/4
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 = 1/2
9
Two coins are tossed. P(no heads)? (two events)
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Only TT → 1/4
10
P(drawing a vowel) from the letters of MATHS? (single)
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Only A → 1/5