Grade 11 Maths · Probability

Calculate from a tree diagram

Find a probability from a tree diagram by multiplying along the branches and adding the paths you need, for example ½ × ⅓ = ⅙.

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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.

More past paper questions: calculate from a tree diagram

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3. Question 9.3.2 · 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 $0, 2 x$ .
9.3.2 If it is given that the overall probability of using sunscreen on a randomly selected day is $0, 62$ , determine the value of $x$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  $0, 7 x + 0, 06 x$ $0, 7 x + 0, 06 x$
  1 mark · Calculate from a tree diagram
2. ✓
  $= 0, 62$ $0, 7 x + 0, 06 x = 0, 62$
  1 mark · Calculate from a tree diagram
3. ✓
  Answer $0, 76 x = 0, 62$
  $x = 0, 82$
  1 mark · Calculate from a tree diagram
4. Question 12.1.2 · September 2024 · Paper 1 · Provincial · 2 marks
12.1 The data obtained from a city's police department indicates that of all motor vehicles reported stolen, 80% were stolen by syndicates to be sold off, and 20% were stolen by individuals for personal use. Of the vehicles presumed stolen by syndicates: 24% were recovered within 48 hours, 16% were recovered after 48 hours, 60% were never recovered. Of those vehicles presumed stolen by individuals: 38% were recovered within 48 hours, 58% were recovered after 48 hours, 4% were never recovered.
12.1.2 Calculate the probability that if a vehicle was stolen in this city, it would be stolen by a syndicate and recovered within 48 hours.(2)
Show the memo (2 ticks)Memo
1. ✓
  Probability calculation $0, 8 \times 0, 24$
  1 mark · Calculate from a tree diagram
2. ✓
  Answer $0, 192$
  1 mark · Calculate from a tree diagram
5. 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
6. Question WE11 · Siyavula Grade 11 Mathematics, 10.4 Tree diagrams, Worked example 11 · 5 marks
WE11 You play the following game. You flip a coin. If it comes up tails, you get $2$ points and your turn ends. If it comes up heads, you get only $1$ point, but you can flip the coin again. If you flip the coin multiple times in one turn, you add up the points. You can flip the coin at most $3$ times in one turn. What is the probability that you will get exactly $3$ points in one turn? Draw a tree diagram to visualise the different possibilities.(5)
Show the memo (5 ticks)Memo
1. ✓
  First level of the treeFirst flip: $H$ ( $1$ pt) with probability $\frac{1}{2}$ ; $T$ ( $2$ pts) with probability $\frac{1}{2}$
  1 mark · Draw a tree diagram
2. ✓
  Second and third levelsOnly after $H$ is the coin flipped again: $H$ then $H$ ( $2$ pts) or $T$ ( $3$ pts); after $H, H$ : $H$ ( $3$ pts) or $T$ ( $4$ pts). Every branch has probability $\frac{1}{2}$ . $Memo diagram$
  1 mark · Draw a tree diagram
3. ✓
  Path (H; T) $(H; T)$ : $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$
  1 mark · Calculate from a tree diagram
4. ✓
  Path (H; H; H) $(H; H; H)$ : $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$
  1 mark · Calculate from a tree diagram
5. ✓
  Answer $P (exactly 3 points) = \frac{1}{4} + \frac{1}{8} = \frac{3}{8}$
  1 mark · Calculate from a tree diagram

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