Grade 11 Maths · Probability · Paper 1

Tree Diagrams Grade 11

Real Tree Diagrams 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: 10 past paper questions
skills: 2 skills
videos: 2 videos

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Question 10 · November 2023 · Paper 1 · Provincial · 4 marks

10 A bag contains

x

balls of which 5 are red and the rest are green. One ball is taken out of the bag randomly and it is not replaced. A second ball is taken out of the bag. The probability of picking both green balls is

\frac{3}{11}

. Show that the probability of picking both green balls can be represented by the equation:

4 x^{2} - 59 x + 165 = 0

.(4)

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

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4. Question 9.3.1 · November 2025 · Paper 1 · Provincial · 3 marks
9.3 During the summer season in South Africa, the probability of sunny weather on any given day is 0,7. If it is sunny, the probability that a person uses sunscreen is $x$ . If it is not sunny, the probability of using sunscreen is $0, 2 x$ .
9.3.1 Draw a tree diagram, clearly labelling the branches and indicating the outcomes.(3)
Show the memo (3 ticks)Memo
1. ✓
  First branches i.e. S and S'First stage: Sunny (S) $0, 7$ and Not sunny (S') $0, 3$ $Memo diagram$
  1 mark · Draw a tree diagram
2. ✓
  Second branches i.e. U and U'After S: U $x$ and U' $1 - x$
  After S': U $0, 2 x$ and U' $1 - 0, 2 x$
  1 mark · Draw a tree diagram
3. ✓
  OutcomesSU: $0, 7 x$ ; SU': $0, 7 (1 - x)$ ; S'U: $0, 06 x$ ; S'U': $0, 3 (1 - 0, 2 x)$
  1 mark · Draw a tree diagram
5. Question WE12 · Siyavula Grade 11 Mathematics, 10.4 Tree diagrams, Worked example 12 · 5 marks
WE12 A person takes part in a medical trial that tests the effect of a medicine on a disease. Half the people are given medicine and the other half are given a sugar pill, which has no effect on the disease. The medicine has a $60%$ chance of curing someone. But, people who do not get the medicine still have a $10%$ chance of getting well. There are $50$ people in the trial and they all have the disease. Talwar takes part in the trial, but we do not know whether he got the medicine or the sugar pill. Draw a tree diagram of all the possible cases. What is the probability that Talwar gets cured?(5)
Show the memo (5 ticks)Memo
1. ✓
  First level of the treeMedicine $\frac{1}{2}$ ; sugar pill $\frac{1}{2}$
  1 mark · Draw a tree diagram
2. ✓
  Second level of the treeMedicine: cured $\frac{3}{5}$ ; not cured $\frac{2}{5}$
  Sugar pill: cured $\frac{1}{10}$ ; not cured $\frac{9}{10}$ $Memo diagram$
  1 mark · Draw a tree diagram
3. ✓
  Path: medicine, cured $\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}$
  1 mark · Calculate from a tree diagram
4. ✓
  Path: sugar pill, cured $\frac{1}{2} \times \frac{1}{10} = \frac{1}{20}$
  1 mark · Calculate from a tree diagram
5. ✓
  Answer $\frac{3}{10} + \frac{1}{20} = \frac{7}{20}$
  The probability that Talwar is cured is $\frac{7}{20}$ .
  1 mark · Calculate from a tree diagram
6. 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
7. 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

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