Grade 11 Maths · Probability

Use the product rule for independence

Multiply probabilities of independent events, P(A and B) = P(A) × P(B), or check whether two events are independent, for example 0,5 × 0,2 = 0,1.

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Gr 11 Probability: Independent eventsKevinmathscience

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Mathematics Grade 11 Probability - Dependent and Independent Events @mathszoneafricanmotivesMaths Zone African Motives

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Question 11.3 · November 2024 · Paper 1 · National (DBE) · 4 marks

A certain number of learners are sitting for examinations in Mathematics (M), Tourism (T) and Geography (G). Total M=22, Total T=16, Total G=18. 5 sit for M and T but not G. 4 sit for M and G but not T. 3 sit for T and G but not M. 6 sit for only T. All learners sit for at least one.

11.3 Determine if the events: sitting for examinations in Mathematics and sitting for examinations in Tourism are independent. Support your answer with the necessary calculations.(4)

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

More past paper questions: use the product rule for independence

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3. 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
4. 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
5. Question 11.2 · September 2024 · Paper 1 · Provincial · 3 marks
Let A and B be two events in a sample space. Suppose that $P (A) = 0, 4$ $P (A or B) = 0, 7$ and $P (B) = k$ .
11.2 For what value of k are A and B independent?(3)
Show the memo (3 ticks)Memo
1. ✓
  Intersection $P (A \cap B) = 0, 4 k$
  1 mark · Use the product rule for independence
2. ✓
  Substitution $0, 7 = 0, 4 + k - 0, 4 k$
  1 mark · Use the addition rule
3. ✓
  Answer $k = 0, 5$
  1 mark · Use the addition rule
6. 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

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