Lesson P8

P8 Independent and dependent combined events Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson P8, Independent and dependent combined events: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 5: Probability, written with Revision Ninja.

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The 20 questions

  1. When are two events independent?

    • The outcome of one does not affect the outcome of the other
    • One event must be certain to happen before the other
    • They always happen at the same time, in every trial
    • They can never occur together in the same single trial

  2. For independent events A and B, what is P(A and B)?

    • P(A) - P(B)
    • P(A) / P(B)
    • P(A) + P(B)
    • P(A) x P(B)

  3. When do you add probabilities of two events?

    • When finding P(not A)
    • When the events are dependent only
    • When finding P(A or B) for mutually exclusive events
    • When finding P(A and B) for independent events

  4. Two draws are made with replacement. Are the two draws independent or dependent?

    • Independent
    • Exhaustive
    • Dependent
    • Mutually exclusive

  5. Two draws are made without replacement. What type of events are they?

    • Impossible
    • Independent
    • Certain
    • Dependent

  6. In a tree diagram, probabilities along branches are multiplied to find what?

    • The probability of that combined path
    • The mean of the outcomes along the branches
    • The median of the outcomes along the whole tree
    • The sum of all the branch probabilities

  7. Which assumption is needed to multiply two probabilities together for a combined event?

    • The events are always mutually exclusive
    • The events are only dependent
    • The events do not affect each other
    • The probabilities are both above 0.5

  8. P(A) = 0.4 and P(B) = 0.5, and the events are independent. What is P(A and B)?

    • 0.1
    • 0.45
    • 0.9
    • 0.2

  9. A coin is tossed twice. What is the probability of two heads?

    • 1/8
    • 1/3
    • 1/4
    • 1/2

  10. A fair dice and a fair coin are used. What is the probability of a 6 and a head?

    • 1/2
    • 1/6
    • 1/12
    • 1/8

  11. A bag has 3 red and 2 blue counters. Two counters are drawn with replacement. What is the probability of red then blue?

    • 3/5
    • 2/5
    • 6/25
    • 6/20

  12. The same bag of 3 red and 2 blue counters is used, but the first counter is not replaced. What is the probability of red then blue?

    • 6/20
    • 6/25
    • 3/4
    • 3/10

  13. Events A and B are independent with P(A) = 0.2 and P(B) = 0.5. What is the probability that neither occurs?

    • 0.3
    • 0.4
    • 0.7
    • 0.1

  14. A coin is tossed three times. What is the probability of three tails?

    • 1/6
    • 1/8
    • 1/3
    • 1/2

  15. A first event has probability 0.3 and the second event, given the first, has probability 0.2. What is the probability that both occur?

    • 0.06
    • 0.5
    • 0.1
    • 0.2

  16. Which statement is correct for dependent events?

    • The probability of B can change depending on whether A has occurred
    • P(A and B) is always zero, since the events cannot both occur
    • P(A and B) always equals P(A) times P(B), whatever happens
    • They are always independent, so no conditional is needed

  17. (H) A fair dice is rolled twice. What is the probability of two sixes?

    • 1/3
    • 1/12
    • 1/6
    • 1/36

  18. (H) A bag has 4 red and 6 blue counters. Two are drawn without replacement. What is the probability that both are blue?

    • 2/5
    • 1/3
    • 9/25
    • 6/25

  19. (H) The probability of rain today is 0.3. Given rain today, the probability of rain tomorrow is 0.6. What is the probability of rain on both days?

    • 0.18
    • 0.9
    • 0.3
    • 0.6

  20. (H) Events A and B are mutually exclusive with P(A) = 0.5 and P(B) = 0.4. What is P(A and B)?

    • 0.45
    • 0.9
    • 0
    • 0.2

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