Grade 11 Maths · Probability · Paper 1

Contingency Tables Grade 11

Real Contingency Tables 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: 11 past paper questions
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Question 2.1 · November 2024 · Paper 2 · Provincial · 2 marks

The weight of the boxers who underwent fitness and health checks is shown in the frequency table below. $Diagram for this question$

2.1 Complete the cumulative frequency column provided in the table in the ANSWER BOOK.(2)

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4. Question 9.1.1 · November 2025 · Paper 1 · Provincial · 2 marks
9.1 A and B are independent events. It is further given that:
• P(A) = 0,3
• P(B) = 0,6
9.1.1 Are the events, A and B mutually exclusive? Motivate your answer.(2)
Show the memo (2 ticks)Memo
1. ✓
  NONO
  1 mark · Use the addition rule
2. ✓
  Valid reasonP(A) $\times$ P(B) $= 0, 3 \times 0, 6 = 0, 18$
  $∴$ P(A and B) $= 0, 18 \neq = 0$
  1 mark · Use the product rule for independence
5. 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
6. Question 9.1.2 · November 2023 · Paper 1 · Provincial · 4 marks
9.1 For any two events A and B, it is given that $P (A) = 0, 35$ and $P (A or B) = 0, 61$ . Determine $P (B)$ if:
9.1.2 A and B are independent.(4)
Show the memo (4 ticks)Memo
1. ✓
  FormulaFor independent events:
  $P (A or B) = P (A) + P (B) - P (A and B)$
  1 mark · Use the addition rule
2. ✓
  Substitution $0, 61 = 0, 35 + P (B) - P (A) \cdot P (B)$
  1 mark · Use the product rule for independence
3. ✓
  $0, 61 = 0, 35 + P (B) - 0, 35 \times P (B)$ $0, 61 = 0, 35 + P (B) - 0, 35 \times P (B)$
  1 mark · Use the product rule for independence
4. ✓
  Answer $0, 61 = 0, 35 + 0, 65 \times P (B)$
  $0, 65 \times P (B) = 0, 26$
  $P (B) = \frac{0 , 26}{0 , 65} = 0, 4$
  1 mark · Use the product rule for independence
7. Question a · Siyavula Grade 11 Mathematics, 11.3 Ogives, Worked example 8 · 1 mark
The grouped data below is given in a table. $Diagram for this question$
a Determine the cumulative frequencies of the grouped data and complete the table.(1)
Show the memo (1 tick)Memo
1. ✓
  Cumulative frequenciesCumulative frequencies: $5$ ; $12$ ; $24$ ; $34$ ; $40$
  1 mark · Read and complete a frequency table

Contingency Tables Grade 11 videos

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

Gr 11 Probability: Independent eventsKevinmathscience

Grade 8 Data Handling: Tally tables and frequency tablesMaths Monkey

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