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Grade 10 · Probability
Probability: Venn Diagrams & the Addition Rule (Grade 10)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    A fair die is rolled. Find P(rolling a 4).
    (1)
  2. 2
    Find P(rolling an even number) on a fair die.
    (1)
  3. 3
    If P(A) = 0,3 find P(not A).
    (1)
  4. 4
    State the addition rule.
    (2)
  5. 5
    If A and B are mutually exclusive, what is P(A and B)?
    (1)
  6. 6
    From the Venn diagram, find P(A and B).
    (2)
    S A B 12 8 10 5 n(S) = 35 · n(A) = 20 · n(B) = 18 · n(A and B) = 8
  7. 7
    From the Venn diagram, find P(A or B).
    (2)
    S A B 12 8 10 5 n(S) = 35 · n(A) = 20 · n(B) = 18 · n(A and B) = 8
  8. 8
    From the Venn diagram, find P(neither A nor B).
    (2)
    S A B 12 8 10 5 n(S) = 35 · n(A) = 20 · n(B) = 18 · n(A and B) = 8
  9. 9
    n(A) = 20 and 8 are in both. How many take ONLY A?
    (2)
    S A B ? 8 10 5 n(S) = 35 · n(A) = 20 · n(B) = 18 · n(A and B) = 8
  10. 10
    A die is rolled 90 times and a 5 comes up 12 times. Calculate the relative frequency of rolling a 5.
    (2)
  11. 11
    For that same die, write down the theoretical probability of rolling a 5 and comment on the difference.
    (2)
  12. 12
    What generally happens to the relative frequency as the number of trials becomes very large?
    (2)
  13. 13
    Give ONE example of a situation where the probability CANNOT be found by counting equally likely outcomes, and say why.
    (2)
TOTAL: 22 marks
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