Grade 10 Maths · Probability

Use the complementary rule

Find the chance that something does not happen by subtracting from 1, for example P(not rain) = 1 − 0,3 = 0,7.

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Gr 11 Probability: Complimentary, mutually inclusiveKevinmathscience

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Question 11.2 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

Consider the three-digit numbers from 501 up to 999.

11.2 Calculate the probability of a three-digit number not satisfying the condition given in QUESTION 11.1.(3)

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More past paper questions: use the complementary rule

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3. Question 11.2.3 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
11.2 The items that a learner bought at a tuck shop were recorded over a period of time. The probabilities of the learner buying a sandwich (S), a chocolate (C) and a juice (J) are shown in the Venn diagram below.
11.2.3 Calculate the probability that the learner would NOT buy any of the three items.(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply the complementary rule to the sum of all internal probabilities $1 - (0, 04 + 0, 02 + 0, 09 + 0, 03 + 0, 01 + 0, 04 + 0, 20)$
  1 mark · Use the complementary rule
2. ✓
  Calculate final answer $0, 57$
  1 mark · Use the complementary rule
4. Question 9.1.2 · November 2024 · Paper 1 · Provincial · 2 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.
9.1.2 Determine the probability that the trespasser will not be detected.(2)
Show the memo (2 ticks)Memo
1. ✓
  $1 - 0, 8$ P(Not detected) $= 1 -$ P(at least detected by one)
  $= 1 - 0, 8$
  1 mark · Use the complementary rule
2. ✓
  Answer $= 0, 2$
  1 mark · Use the complementary rule
5. Question 8.1 · November 2024 · Paper 1 · Provincial · 2 marks
Consider events A and B. $P (A) = 0, 43$ , $P (B) = 0, 37$ and $P (A and B) = 0, 1591$ .
8.1 Determine whether events A and B are complimentary.(2)
Show the memo (2 ticks)Memo
1. ✓
  Sum the probabilities $P (A) + P (B) = 0, 43 + 0, 37 = 0, 80$
  1 mark · Use the complementary rule
2. ✓
  Conclusion $0, 80 \neq = 1$ . Not complementary events.
  1 mark · Use the complementary rule
6. Question 3.1.1 · September 2024 · Provincial · 1 mark
3.1 Given: $P (A) = 0, 4$ ; $P (B) = 0, 5$ and $P (A and B) = 0, 25$ . Determine the:
3.1.1 $P (not B)$ (1)
Show the memo (1 tick)Memo
1. ✓
  Calculate complement $P (not B) = 1 - P (B) = 1 - 0, 5 = 0, 5$
  1 mark · Use the complementary rule

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