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CAIE A Level Mathematics 9709

Probability questions

Exam-style questions on Probability, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationA bag contains 5 counters, 2 of which are red. One counter is taken at random. Find the probability that it is red.
  2. 2 marksFoundationA bag contains 3 red marbles and 9 blue marbles. One marble is chosen at random. Find the probability that the marble is red.
  3. 3 marksStandardThe probabilities of events A and B are given in the table below. Event Probability A frac35 B frac12 A ∩ B frac15 (i) Find P(A) × P(B) as an exact fraction. (ii) Hence determine whether events A and B are independent.
  4. 3 marksStandardA survey of students recorded their gender and whether they passed a test. The results are shown in the table below. Passed Failed Total Male 4 8 12 Female 6 14 20 Total 10 22 32 A student is selected at random.
  5. 3 marksStandardThe two-way table below shows the number of people who own a cat and who own a dog. Dog No dog Cat 3 4 No cat 2 1 One person is chosen at random.
  6. 3 marksStandardA bag contains 4 red marbles and 2 blue marbles. Two marbles are drawn at random without replacement. Find the probability that both marbles are red.
  7. 3 marksStandardA bag contains 4 red balls and 4 blue balls. A ball is drawn at random, its colour noted, and then replaced. A second ball is then drawn at random. Find the probability that both balls are red. Give your answer correct…
  8. 4 marksChallengeIn a school, the probability that a randomly selected student is in Year 10 is 0.25. If the student is in Year 10, the probability that they study Physics is 0.6. If the student is in Year 11, the probability that they…
  9. 4 marksChallengeA factory uses two machines, A and B, to produce items. Machine A produces a proportion 0.75 of the items, and machine B produces the rest. The probability that an item from machine A is defective is 0.2, and the…