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Chapter 5 Practice Paper: Probability — question paper

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QQ/S4EM/CH5

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 5 Practice Paper

Probability

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 5 (S2 probability: single events, possibility diagrams, tree diagrams with and without replacement, mutually exclusive and independent events).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

  1. 1

    A fair spinner has eight equal sectors numbered 1 to 8. The spinner is spun once.

    1. (a)

      Find the probability of landing on 7.

      P(7) =[1]
    2. (b)

      Find the probability of landing on an even number.

      P(even) =[1]
    3. (c)

      Find the probability of landing on a square number.

      [2]
  2. 2

    Two fair dice are rolled and their sum recorded. A possibility diagram may help.

    1. (a)

      Explain why the experiment has 36 equally likely outcomes.

      [1]
    2. (b)

      Find the probability that the sum is 6.

      [2]
    3. (c)

      Find the probability that the sum is greater than 9.

      [2]
  3. 3

    A bag contains 4 red and 3 blue counters. Two counters are drawn at random, one after the other, without replacement.

    1. (a)

      Write the probabilities on each branch of a fully labelled tree diagram.

      [2]
    2. (b)

      Find the probability that the two counters have the same colour.

      [3]
  4. 4

    In a board game, a player wins a challenge with probability 0.3. The player attempts the challenge twice. Each attempt is independent.

    1. (a)

      Draw a tree diagram for the two attempts.

      [1]
    2. (b)

      Find the probability that the player wins exactly one of the two attempts.

      [2]
    3. (c)

      Hence write down the probability that the player wins at least one attempt.

      P =[1]
  5. 5

    In a class of 25 students, 15 study physics, 12 study chemistry and 5 study both. A student is chosen at random.

    1. (a)

      Find the probability that the student studies both subjects.

      P(both) =[1]
    2. (b)

      Find the probability that the student studies physics but not chemistry.

      [2]
    3. (c)

      Find the probability that the student studies neither subject.

      [2]
  6. 6

    A carton of 10 memory cards contains 4 defective cards. Three cards are taken at random, one after another, without replacement.

    1. (a)

      Show that the probability that the first card is defective and the other two are not is 1/6.

      [2]
    2. (b)

      Hence find the probability that exactly one of the three cards is defective.

      [2]
    3. (c)

      Find the probability that at least one of the three cards is defective.

      [3]

— End of paper —