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Topic 17 Practice Paper: Probability — question paper

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QQ/IGCSE-MATHS/T17

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 17 Practice Paper

Probability

Duration: 40 minutes
Total: 30 marks
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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.
  • 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 against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 17: the probability scale and complements, relative and expected frequency, sample space diagrams, Venn diagrams, tree diagrams with and without replacement, at-least-one complements, and conditional probability from two-way tables.

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

    A whole number from 1 to 20 is picked at random. P(multiple of 5) is

    1. A¼
    2. B1⁄10
    3. C⅕
    4. D1⁄20
    ( )
  2. 2

    A coin is flipped three times. P(three tails) is

    1. A⅛
    2. B⅙
    3. C¼
    4. D⅜
    ( )
  3. 3

    A bag holds 6 white and 9 black counters. One is drawn. P(black) is

    1. A⅔
    2. B⅖
    3. C⅓
    4. D⅗
    ( )
  4. 4

    P(rain tomorrow) = 0.35. P(no rain tomorrow) is

    1. A0.35
    2. B0.65
    3. C0.55
    4. D0.75
    ( )
  5. 5

    A fair die is rolled 90 times. The expected number of fours is

    1. A10
    2. B12
    3. C15
    4. D18
    ( )
  6. 6

    Two fair coins are flipped. P(one head and one tail) is

    1. A½
    2. B¼
    3. C⅓
    4. D¾
    ( )
  7. 7

    A spinner wins each go with probability 0.2. In two independent goes, P(win both) is

    1. A0.4
    2. B0.2
    3. C0.08
    4. D0.04
    ( )
  8. 8

    A bag holds 3 red and 5 green counters. Two are drawn with replacement. P(both green) is

    1. A9⁄64
    2. B25⁄64
    3. C5⁄14
    4. D15⁄64
    ( )
  9. 9

    A darts player hits the bullseye with probability 0.7. In two throws, P(exactly one bullseye) is

    1. A0.49
    2. B0.21
    3. C0.42
    4. D0.91
    ( )
  10. 10

    Two events: the chance of A is 0.6, the chance of B is 0.5, and both occur with probability 0.35. The chance of A or B occurring is

    1. A0.75
    2. B1.1
    3. C0.85
    4. D0.45
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    A lucky dip contains 30 tickets, of which 12 are winning tickets.

    1. (a)

      Find the probability of winning on a single dip.

      [1]
    2. (b)

      A ticket is dipped, then replaced, and a second dip is made. Find P(two winning dips).

      [2]
    3. (c)

      Find P(at least one of the two dips wins).

      [2]
  2. 12

    A keyring holds three similar-looking keys, of which exactly one opens a door. The key is tried, and if it fails it is replaced and the try repeated.

    1. (a)

      Write down the theoretical probability that one try opens the door.

      [1]
    2. (b)

      In 120 tries the door opens 46 times. Calculate the relative frequency, giving your answer to 3 decimal places.

      [2]
    3. (c)

      Comment on whether the experiment is consistent with the theoretical probability.

      [2]
  3. 13

    A purse contains 4 gold and 6 silver coins. Two coins are taken out one after the other, and the first is not put back. (Extended)

    1. (a)

      Find P(both coins are gold).

      [2]
    2. (b)

      Find P(the two coins are the same colour).

      [3]
  4. 14

    Of 50 athletes, 30 follow a new training plan and 20 do not. 24 of the trained athletes completed a marathon, along with 8 of the untrained athletes. (Extended)

    1. (a)

      Complete the two-way table (trained / not trained against completed / did not complete).

      [2]
    2. (b)

      One athlete is chosen at random. Find P(completed).

      [1]
    3. (c)

      Given that an athlete completed the marathon, find the probability that they followed the training plan.

      [2]

— End of paper —