Practice Maths

Topic Review — Probability

Mixed Practice — L41 – L44

This review covers all lessons in the Probability topic. Try each question before checking your answers.

Review Questions

  1. Single event probability. Fluency

    1. A bag contains 4 red, 6 blue, and 2 white marbles. A marble is drawn at random. Find: (i) P(red)   (ii) P(blue)   (iii) P(white)   (iv) P(not blue)
    2. A standard die is rolled once. Find: (i) P(odd number)   (ii) P(greater than 2)   (iii) P(not a 4)
    3. A card is drawn from a standard 52-card deck. Find: (i) P(ace)   (ii) P(red face card)   (iii) P(not a heart)
    4. A spinner has 8 equal sections numbered 1 to 8. Find: (i) P(prime number)   (ii) P(factor of 8)   (iii) P(greater than 6)

  2. Complementary events. Fluency

    1. P(A) = 0.42. Find P(A′).
    2. P(B′) = 7/12. Find P(B).
    3. A coin is flipped. Find P(not tails).
    4. P(raining tomorrow) = 35%. Find P(not raining).
    5. Three mutually exclusive and exhaustive events: P(A) = 0.15, P(B) = 0.45. Find P(C).
    6. A quality test finds P(defective) = 0.03. In a batch of 400, how many are expected to be non-defective?

  3. Tree diagrams and two-step experiments. Understanding

    1. A fair coin is flipped and then a standard die is rolled. Draw a tree diagram (or describe the sample space). How many outcomes are there in total?
    2. A spinner has sections Red (R) and Blue (B) in ratio 1:1. It is spun twice. Find: (i) P(Red then Red)   (ii) P(at least one Blue)
    3. A bag has 3 green and 2 orange marbles. Two marbles are drawn without replacement. Find: (i) P(both green)   (ii) P(one of each colour)
    4. Two dice are rolled. Find: (i) P(both show a 3)   (ii) P(the sum equals 7)   (iii) P(the sum is less than 4)

  4. Experimental probability and relative frequency. Understanding

    1. A coin is flipped 80 times; heads appears 44 times. Find the experimental probability of heads. Compare to the theoretical probability.
    2. In 50 spins of a spinner, the colour red appeared 18 times. Find: (i) the relative frequency of red (ii) the expected number of reds in 200 spins (using this frequency)
    3. A die is rolled 120 times. How many times would you theoretically expect to roll a number less than 3?
    4. A sample of 300 light bulbs had 15 found to be faulty. Estimate P(faulty) and predict the number of faulty bulbs in a batch of 2 000.

  5. Mixed probability problem solving. Problem Solving

    1. At a school event, students randomly choose one activity from {Art, Drama, Science} and one snack from {Apple, Banana}. Find: (i) the total number of equally likely combinations (ii) P(Drama and Banana) (iii) P(not Art)
    2. A bag has 5 red and 3 blue marbles. Two are drawn without replacement.
      1. Find P(both the same colour).
      2. Find P(at least one red).
    3. A school basketball player has an experimental P(scoring a free throw) = 0.72 based on 100 attempts. In a tournament she attempts 25 free throws. How many would you expect her to score? How many would you expect her to miss?
    4. Explain the difference between theoretical probability and experimental probability, and give one example of a situation where only experimental probability can be used.
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