Grade 11 Maths · Paper 1

Probability Grade 11

Real past paper questions and answers from 2023 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 34 past paper questions
skills: 8 skills
videos: 8 videos

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Question 10.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

10.1 A and B are mutually exclusive events. If

P (A) = 0, 42

and

P (A or B) = 0, 79

, calculate

P (B)

.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

What's in Probability Grade 11

Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.

Probability Notation9 past paper questions

Dependent and Independent Events11 past paper questions

Venn Diagrams7 past paper questions

Tree Diagrams10 past paper questions

Contingency Tables11 past paper questions

More Probability Grade 11 questions and answers

Try each one on paper before you open the memo.

1. Question 11.2.2 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
11.2 The items that a learner bought at a tuck shop were recorded over a period of time. The probabilities of the learner buying a sandwich (S), a chocolate (C) and a juice (J) are shown in the Venn diagram below.
11.2.2 Calculate the probability that the learner will buy at least two of the three items.(2)
Show the memo (1 tick)Memo
1. ✓
  Add the probabilities of the regions in two or three circles $P (at least two) = 0, 02 + 0, 01 + 0, 03 + 0, 04 = 0, 1$
  2 marks · Find probability from a Venn diagram
2. Question 9.2.2 · November 2025 · Paper 1 · Provincial · 4 marks
9.2 The contingency table below represents 106 athletes' responses regarding jogging on the sand.

Answer the questions that follow. $Diagram for question 9.2$
9.2.2 Is the event "enjoy jogging on sand" independent of the gender?(4)
Show the memo (4 ticks)Memo
1. ✓
  P(Enjoy jogging) $\times$ P(Male)P(Enjoy jogging) $= \frac{56}{106}$ ; P(Male) $= \frac{42}{106}$
  P(Enjoy jogging) $\times$ P(Male) $= \frac{56}{106} \times \frac{42}{106}$
  1 mark · Use the product rule for independence
2. ✓
  Answer $= 0, 20932...$
  1 mark · Use the product rule for independence
3. ✓
  P(Enjoy jogging and Male)P(Enjoy jogging and Male) $= \frac{26}{106} = 0, 24528...$
  1 mark · Calculate a simple probability
4. ✓
  ConclusionP(Enjoy jogging and Male) $\neq =$ P(Enjoy jogging) $\times$ P(Male)
  $∴$ Events are not independent.
  1 mark · Use the product rule for independence
3. Question 9.1.1 · November 2024 · Paper 1 · Provincial · 3 marks
9.1 A certain company uses a camera detector system to detect trespassers. Two independent cameras, A and B are installed, one at the front main gate and the other one at the back of the building. If someone trespasses, the probability that the person will be detected by camera A is 0,5 and the probability that the person will be detected by camera B is 0,6.

Answer the questions that follow.
9.1.1 If there is a trespasser, what is the probability that the trespasser will be detected by at least one camera?(3)
Show the memo (3 ticks)Memo
1. ✓
  $0, 5 \times 0, 6$ At least detected by one camera $\Rightarrow$ A or B
  P(A and B) $= 0, 5 \times 0, 6$
  1 mark · Use the product rule for independence
2. ✓
  Substitution into the correct formulaP(A or B) $=$ P(A) $+$ P(B) $-$ P(A and B)
  $= 0, 5 + 0, 6 - (0, 5 \times 0, 6)$
  1 mark · Use the addition rule
3. ✓
  Answer $= 0, 8$
  1 mark · Use the addition rule
4. Question WE10 · Siyavula Grade 11 Mathematics, 10.4 Tree diagrams, Worked example 10 · 5 marks
WE10 If it rains on a given day, the probability that it rains the next day is $\frac{1}{3}$ . If it does not rain on a given day, the probability that it rains the next day is $\frac{1}{6}$ . The probability that it will rain tomorrow is $\frac{1}{5}$ . What is the probability that it will rain the day after tomorrow? Draw a tree diagram of all the possibilities to determine the answer.(5)
Show the memo (5 ticks)Memo
1. ✓
  First level of the treeTomorrow: rain $\frac{1}{5}$ ; no rain $\frac{4}{5}$
  1 mark · Draw a tree diagram
2. ✓
  Second level of the treeAfter rain: rain $\frac{1}{3}$ ; no rain $\frac{2}{3}$
  After no rain: rain $\frac{1}{6}$ ; no rain $\frac{5}{6}$ $Memo diagram$
  1 mark · Draw a tree diagram
3. ✓
  Path: rain, rain $P (rain tomorrow and rain day after tomorrow) = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$
  1 mark · Calculate from a tree diagram
4. ✓
  Path: no rain, rain $P (not rain tomorrow and rain day after tomorrow) = \frac{4}{5} \times \frac{1}{6} = \frac{2}{15}$
  1 mark · Calculate from a tree diagram
5. ✓
  Answer $P (rain day after tomorrow) = \frac{1}{15} + \frac{2}{15} = \frac{1}{5}$
  1 mark · Calculate from a tree diagram
5. Question b · Siyavula Grade 12 Mathematics, 10.3 Tools and techniques, Worked example 8 · 2 marks
The probability that the floor of a supermarket will be wet when it opens in the morning is $30%$ and there is a $10%$ probability of the floor being very wet. The probability that a person will slip and fall if the floor is dry is $12%$ and a person is three times as likely to fall if the floor is wet. If the floor is very wet, the probability that a person will fall is $0, 6$ . Draw a tree diagram to represent the given information, showing the probabilities of each outcome, and use it to answer the following questions.
b What is the probability that a person will fall on any given day?(2)
Show the memo (2 ticks)Memo
1. ✓
  Products along the fall paths $P (very wet and fall) = 0, 1 \times 0, 6 = 0, 06$
  $P (wet and fall) = 0, 3 \times 0, 36 = 0, 108$
  $P (dry and fall) = 0, 6 \times 0, 12 = 0, 072$
  1 mark · Calculate from a tree diagram
2. ✓
  Answer $P (fall) = 0, 06 + 0, 108 + 0, 072 = 0, 24$
  The probability of falling on a given day is $24%$ .
  1 mark · Calculate from a tree diagram

Probability Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Gr 11 Probability: Complimentary, mutually inclusiveKevinmathscience

Gr 11 Probability: Probability A or BKevinmathscience

Probability Grade 10 | Tree DiagramKevinmathscience

Gr 11 Probability: Independent eventsKevinmathscience

Probability Grade 10 | Venn DiagramKevinmathscience

Probability Grade 10 | Venn Diagram PracticeKevinmathscience

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