Grade 10 · CAPS

Grade 10 Probability

Maths practice questions and a worked example

Grade 10 Probability covers the addition rule for combined events, complementary and mutually exclusive events, and representing real scenarios with a Venn diagram. Sourced from real November 2022-2023 Paper 1 questions, including the two-bank-membership style Venn-diagram problem that appears across multiple papers in slightly different forms.

Worked example

7.1 For any two events, A and B, it is given that P(A) = 0.25, P(B) = 0.89 and P(A or B)' = 0.05. 7.1.1 Calculate P(A or B).

Answer & explanation

P(A or B) = 1 − P(A or B)' = 1 − 0,05 = 0,95
To find the probability of either event A or event B occurring, we use the complement rule. The complement of the event "A or B" is given as 0.05. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Therefore, we calculate: 1. Identify the complement: P(A or B)' = 0.05. 2. Use the complement rule: P(A or B) = 1 - P(A or B)'. 3. Substitute the given value: P(A or B) = 1 - 0.05. 4. Calculate: P(A or B) = 0.95. Thus, the probability of either event A or event B occurring is 0.95.

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Probability

Question 1 of 3

7.1 A bag contains 3 green balls and 5 red balls. The balls are placed in a bag and one is chosen at random. Determine the probability that the ball selected is red.

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More practice questions

Explore additional Grade 10 Probability questions.

  • 2
    7.1.2 For any two events, A and B, it is given that P(A) = 0,25, P(B) = 0,89 and P(A or B)' = 0,05. Are the two events mutually exclusive? Justify your answer.
  • 3
    7.1.3 For any two events, A and B, it is given that P(A) = 0,25, P(B) = 0,89 and P(A or B)' = 0,05. Calculate P(A and B).
  • 4
    7.1.4 For any two events, A and B, it is given that P(A) = 0,25, P(B) = 0,89 and P(A or B)' = 0,05. What is the probability of event B only?
  • 5
    7.2.1 In a small town of 1 500 people, there are two main banks, Add Savings and Multiplier Bank. Most of the people in the town bank with one or both of these banks. 600 people bank with Add Savings and 950 bank with Multiplier Bank. 235 people in the town do not use either Add Savings or Multiplier Bank. Draw a Venn diagram to illustrate the information given above.

Common mistakes

  • Double-counting the overlap region when adding P(A) and P(B) instead of subtracting P(A and B), and forgetting that complementary events must sum to exactly 1.

More Grade 10 Maths topics

Aligned to CAPS Grade 10 Maths — Probability. Curriculum source: CAPS for the FET Phase, Department of Basic Education.

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