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Grade 12 · Probability
Counting Principles & Probability (Grade 12)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    How many 4-digit PINs can be formed if digits may repeat?
    (2)
  2. 2
    How many 4-digit PINs can be formed if no digit may repeat?
    (2)
  3. 3
    In how many ways can 5 different books be arranged on a shelf?
    (1)
  4. 4
    4 boys and 3 girls sit in a row. In how many ways can they sit if the girls sit together?
    (3)
  5. 5
    For those 7 learners, calculate the probability that the girls sit together.
    (2)
  6. 6
    How many arrangements are there of the letters of the word LETTER?
    (3)
  7. 7
    Write down the value of 0!
    (1)
  8. 8
    Using the tree diagram below, calculate the probability that a person tests positive.
    (3)
    1545910110210810DD′TT′TT′has diseasetest result
  9. 9
    Of 80 learners: 40 play soccer, 32 play cricket, 28 play tennis; 15 play soccer and cricket, 12 soccer and tennis, 10 cricket and tennis, and 6 play all three. How many play none?
    (4)
  10. 10
    In a group of 150 people, 90 are female and 60 wear glasses, of whom 40 are female. Determine whether ‘female’ and ‘wears glasses’ are independent.
    (4)
  11. 11
    State the test for two events being independent.
    (2)
  12. 12
    Why must a three-event Venn diagram be filled from the centre outwards?
    (2)
TOTAL: 29 marks
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