Grade 11 Maths · Probability · Paper 1

Dependent and Independent Events Grade 11

Real Dependent and Independent Events 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.

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videos: 2 videos

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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)

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

Dependent and Independent Events skills

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More Dependent and Independent Events Grade 11 questions and answers

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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 12 Mathematics, 10.3 Tools and techniques, Worked example 8 · 3 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.
a Draw the tree diagram.(3)
Show the memo (3 ticks)Memo
1. ✓
  First level: state of the floorVery wet $0, 1$ ; wet $0, 3$ ; dry $1 - 0, 1 - 0, 3 = 0, 6$
  1 mark · Draw a tree diagram
2. ✓
  Second level: wet and dryWet: fall $3 \times 0, 12 = 0, 36$ ; not fall $0, 64$
  Dry: fall $0, 12$ ; not fall $0, 88$
  1 mark · Draw a tree diagram
3. ✓
  Second level: very wetVery wet: fall $0, 6$ ; not fall $0, 4$ $Memo diagram$
  1 mark · Draw a tree diagram
8. Question 10 · November 2024 · Paper 1 · Provincial · 8 marks
Bennie has two fair spinners. (Circles are divided into 3 and 8 equal parts, respectively), as shown below. $Diagram for this question$
10 Bennie is going to spin both spinners. What is the probability that it lands on the same colour after spinning each spinner once?(8)
Show the memo (8 ticks)Memo
1. ✓
  $\frac{1}{3}$ (Red on spinner 1)P(Red on spinner 1) $= \frac{1}{3}$ $Memo diagram$
  1 mark · Draw a tree diagram
2. ✓
  $\frac{3}{8}$ (Red on spinner 2)P(Red on spinner 2) $= \frac{3}{8}$
  1 mark · Draw a tree diagram
3. ✓
  $\frac{1}{8}$ $\frac{1}{3} \times \frac{3}{8} = \frac{1}{8}$
  1 mark · Calculate from a tree diagram
4. ✓
  $\frac{1}{3}$ (Blue on spinner 1)P(Blue on spinner 1) $= \frac{1}{3}$
  1 mark · Draw a tree diagram
5. ✓
  $\frac{5}{8}$ (Blue on spinner 2)P(Blue on spinner 2) $= \frac{5}{8}$
  1 mark · Draw a tree diagram
6. ✓
  $\frac{5}{24}$ $\frac{1}{3} \times \frac{5}{8} = \frac{5}{24}$
  1 mark · Calculate from a tree diagram
7. ✓
  Addition $∴ \frac{5}{24} + \frac{1}{8}$
  1 mark · Calculate from a tree diagram
8. ✓
  Answer $= \frac{5}{24} + \frac{3}{24} = \frac{1}{3}$
  P(same colour) $= \frac{1}{3}$ or $\approx 0, 33$
  1 mark · Calculate from a tree diagram

Dependent and Independent Events Grade 11 videos

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Probability Grade 10 | Tree DiagramKevinmathscience

Gr 11 Probability: Independent eventsKevinmathscience

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