Grade 10 Probability — How to Identify the Question Type

Grade 10 probability questions use basic counting, Venn diagrams, and the addition rule. Before answering, identify whether the question asks for a probability (fraction between 0 and 1) or a count (a whole number).

Type 1: Basic probability from a sample space

Trigger words: "Find the probability", "P(A)", "What is the probability that"

Trigger structure: A list, table, or description gives all possible outcomes. You must find P(A) = number of favourable outcomes ÷ total outcomes.

Do not confuse with: Counting questions — if the question asks 'how many', give a whole number, not a fraction.

Method (no numbers — just the steps)

List or count the total number of outcomes in the sample space
Count the number of outcomes that match the event A
Calculate P(A) = n(A) / n(S)
Leave the answer as a fraction, decimal, or percentage as instructed

Grade 10Paper 1Level 1 — Knowledge

12.1 A bag contains 3 red, 5 blue, and 2 green balls. A ball is drawn at random. Calculate the probability that it is blue.

Source: DBE Mathematics Paper 1, November 2018, Question 12.1

See the progression — same type, increasing difficulty

Easy

A die is rolled. What is the probability of rolling a number greater than 4?

Practice question — not sourced from a past paper.

Medium

The letters of the word MATHEMATICS are written on separate cards and placed in a bag. A card is drawn at random. Find the probability that it shows a vowel.

Practice question — not sourced from a past paper.

Hard

A number is chosen at random from the integers 1 to 20. Find the probability that the number is divisible by 3 or by 5.

Practice question — not sourced from a past paper.

Type 2: Venn diagram problems

Trigger words: "Draw a Venn diagram", "Use the Venn diagram", "n(A ∩ B)"

Trigger structure: Two or more overlapping events are described. Information is given about their intersection or union.

Do not confuse with: A basic list probability — Venn diagrams are needed when two events share outcomes.

Method (no numbers — just the steps)

Draw two overlapping circles labelled A and B inside a rectangle (sample space S)
Fill in the intersection n(A ∩ B) first
Fill in the remaining parts of A and B
Fill in the region outside both circles (neither event)
Check all values sum to n(S)

Grade 10Paper 1Level 3 — Complex Procedures

In a class of 30 learners, 18 play soccer, 12 play basketball, and 5 play both. Draw a Venn diagram and find the probability that a randomly chosen learner plays neither sport.

Practice question — not sourced from a past paper.

Common mistake

Placing the intersection value into only one circle — the value inside the overlap counts towards both A and B.

See the progression — same type, increasing difficulty

Easy

S = {1; 2; 3; 4; 5; 6; 7; 8; 9; 10}. A = {even numbers}, B = {multiples of 3}. List A ∩ B and find P(A ∩ B).

Practice question — not sourced from a past paper.

Medium

50 learners were surveyed. 30 like Maths, 25 like Science, and 10 like both. Draw a Venn diagram and find the probability that a learner likes only Maths.

Practice question — not sourced from a past paper.

Hard

P(A) = 0.5, P(B) = 0.4, and P(A ∪ B) = 0.7. Determine P(A ∩ B) and state whether A and B are mutually exclusive.

Practice question — not sourced from a past paper.

Type 3: Complementary events

Trigger words: "P(not A)", "P(A')", "The probability that ... does NOT happen"

Trigger structure: The question asks for the probability of something NOT occurring.

Method (no numbers — just the steps)

Recall: P(A') = 1 − P(A)
Find P(A) first if it is not given
Subtract from 1

Grade 10Paper 1Level 1 — Knowledge

The probability that it rains on any given day in July is 0,3. Find the probability that it does NOT rain on a randomly chosen day in July.

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy

A card is drawn from a standard deck of 52 cards. P(heart) = 1/4. What is P(not a heart)?

Practice question — not sourced from a past paper.

Medium

A bag contains red and blue balls. P(red) = 3/7. What is the probability of drawing a blue ball?

Practice question — not sourced from a past paper.

Hard

The probability that a learner passes Maths is 0.65 and the probability that a learner passes Science is 0.7. The probability that a learner passes both is 0.5. Find the probability that the learner fails both subjects.

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.