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Chapter 19 Practice Paper: Probability — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH19

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 19 Practice Paper

Probability

Duration: 40 minutes
Total: 30 marks
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Class:
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • Give fractions in their simplest form unless a decimal is requested.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 19: the probability scale and complements, theoretical probability and relative frequency, expected frequency, mutually exclusive and exhaustive events, Venn diagrams with set notation, frequency trees, two-way tables, and tree diagrams for independent, dependent and conditional events.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    The probability of an event that is certain to happen is

    1. A1
    2. B0
    3. C0.5
    4. D100
    ( )
  2. 2

    A fair die is rolled. P(even number) is

    1. A⅓
    2. B½
    3. C⅔
    4. D⅙
    ( )
  3. 3

    P(rolling a 3) = 1⁄6, so P(not rolling a 3) is

    1. A1⁄3
    2. B5⁄6
    3. C1⁄5
    4. D⅙
    ( )
  4. 4

    An experiment is repeated 250 times and each trial succeeds with probability 0.3. The expected number of successes is

    1. A750
    2. B25
    3. C0.3
    4. D75
    ( )
  5. 5

    Mutually exclusive events have P(A) = 0.4 and P(B) = 0.25. P(A or B) is

    1. A0.65
    2. B0.15
    3. C0.1
    4. D1
    ( )
  6. 6

    Of 30 pupils, 18 study maths, 15 study science and 6 study both. n(maths ∪ science) is

    1. A33
    2. B27
    3. C9
    4. D39
    ( )
  7. 7

    Two coins are tossed together. The chance of a double heads is

    1. A½
    2. B⅓
    3. C1
    4. D¼
    ( )
  8. 8

    Three red and two blue counters are drawn from a bag one after another, without replacement. P(both red) is

    1. A9⁄25
    2. B⅖
    3. C0.3
    4. D0.6
    ( )
  9. 9

    In set notation, ∈ means

    1. Ais a member of
    2. Bis not a member of
    3. Cis the complement of
    4. Dis the empty set
    ( )
  10. 10

    P(on time) = 0.6 and P(undamaged | on time) = 0.95. P(on time and undamaged) is

    1. A1.55
    2. B0.35
    3. C0.57
    4. D0.95
    ( )

Section B: Structured questions[20 marks]

Show all your working. Fractions should be given in their simplest form.

  1. 11

    A five-sector spinner.

    1. (a)

      A spinner has 5 equal sectors: 2 red and 3 blue. Find P(red).

      [2]
    2. (b)

      The spinner is spun 150 times. How many reds would you expect?

      [2]
  2. 12

    Netball and hockey.

    1. (a)

      In a class of 28, 16 play netball, 11 play hockey and 5 play both. Find how many play only netball and how many play only hockey.

      [2]
    2. (b)

      Find the probability that a pupil chosen at random plays neither sport.

      [2]
  3. 13

    Two picks, coin replaced.

    1. (a)

      A bag holds 4 white and 6 black counters. One is drawn, replaced, then a second is drawn. Find P(white, white).

      [2]
    2. (b)

      Find P(exactly one white).

      [2]
  4. 14

    Sweets without replacement. (Higher)

    1. (a)

      A tube holds 5 lemon and 3 mint sweets. Two are eaten one after the other. Find P(lemon, mint).

      [2]
    2. (b)

      Find P(the two sweets are the same flavour).

      [2]
  5. 15

    Buses and lateness. (Higher)

    1. (a)

      A student takes the bus with probability 0.4; bus journeys are late with probability 0.3, while other journeys are late with probability 0.1. Find P(bus and late).

      [2]
    2. (b)

      Find P(late).

      [2]

— End of paper —