Unit E: Statistics and Probability

Chapter 2: Probability

Practice


Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.
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  1. Yannick has a spinner that is divided into four equal parts. He performed an experiment and spun the spinner 60 times. He recorded his results in the table below.

    Outcome Frequency
    green
    		19
    yellow 16
    red 10
    blue 15
    total 60




    1. Calculate the theoretical probability of the spinner landing on green.
    2. Calculate the theoretical probability of the spinner landing on each of the other colours.
    3. Calculate the experimental probability of the spinner landing on green. How does the experimental probability compare to the theoretical probability?
    4. Calculate the experimental probability of the spinner landing on blue. How does the experimental probability compare to the theoretical probability?

  2. A bag of hard candy has a total of 12 candies: 2 grape, 3 orange, 3 lemon, and 4 watermelon.







    1. Calculate the theoretical probability of choosing a watermelon candy.
    2. Calculate the theoretical probability of choosing a watermelon candy or an orange candy.
    3. One candy was randomly chosen from the bag of candies and then put back in the bag. A total of 40 trials were completed. The data was recorded in the table below.

      Outcome Frequency
      grape
      		7
      orange
      		8
      lemon
      		14
      watermelon
      		11
      total 40



      Calculate the experimental probability of choosing a watermelon candy.

    4. The experiment is continued until 400 trials were performed.

      Outcome Frequency
      grape
      		65
      orange
      		198
      lemon
      		102
      watermelon
      		135
      total 400




      Calculate the experimental probability of choosing a watermelon candy after 400 trials.

    5. When would the theoretical probability be expected to be equal to the experimental probability?
Yannick has a spinner that is divided into four equal parts. He performed an experiment and spun the spinner 60 times. He recorded his results in the table below.

Outcome Frequency
green
19
yellow 16
red 10
blue 15
total 60




  1. Calculate the theoretical probability of the spinner landing on green.
  2. Calculate the theoretical probability of the spinner landing on each of the other colours.
  3. Calculate the experimental probability of the spinner landing on green. How does the experimental probability compare to the theoretical probability?
  4. Calculate the experimental probability of the spinner landing on blue. How does the experimental probability compare to the theoretical probability?


  1. probability = number   of   green   sections total   number   of   sections = 1 4 = 0 . 25
    Note: the first line of the formula is omitted in the solution of the practice questions because it is not required to be included on the assignment.


    The theoretical probability of the spinner landing on green is 0.25.

  2. Since the spinner is separated into four equal sections, the probability of landing on each of the other sections is also 0.25.

  3. The experimental probability is calculated based on data collected in an experiment.

    probability = number   of   times   landing   on   green total   number   of   spins = 19 60 = 0 . 317

    The experimental probability is 0.317, and the theoretical probability is 0.25. The experimental probability is higher.

  4. The experimental probability is calculated based on data collected in an experiment.

    probability = number   of   times   landing   on   blue total   number   of   spins = 15 60 = 1 4 = 0 . 25

    The experimental probability is 0.25, and the theoretical probability is 0.25. Therefore, they are equal. It is unusual for the experimental probability to equal the theoretical probability after 60 trials.
A bag of hard candy has a total of 12 candies: 2 grape, 3 orange, 3 lemon, and 4 watermelon.






  1. Calculate the theoretical probability of choosing a watermelon candy.
  2. Calculate the theoretical probability of choosing a watermelon candy or an orange candy.
  3. One candy was randomly chosen from the bag of candies and then put back in the bag. A total of 40 trials were completed. The data was recorded in the table below.

    Outcome Frequency
    grape
    		7
    orange
    		8
    lemon
    		14
    watermelon
    		11
    total 40



    Calculate the experimental probability of choosing a watermelon candy.

  4. The experiment is continued until 400 trials were performed.

    Outcome Frequency
    grape
    		65
    orange
    		198
    lemon
    		102
    watermelon
    		135
    total 400



    Calculate the experimental probability of choosing a watermelon candy after 400 trials.

  5. When would the theoretical probability be expected to be equal to the experimental probability?


  1. probability = number   of   watermelon   candies total   number   of   candies = 4 12 = 1 3 = 0 . 333



    The theoretical probability of choosing a watermelon candy is 0.333.

  2. probability = number   of   watermelon   candies + number   of   orange   candies total   number   of   candies = 4 + 3 12 = 7 12 = 0 . 583


    The theoretical probability of choosing a watermelon candy or an orange candy is 0.583.

  3. probability = number   of   watermelon   candies total   number   of   trials = 11 40 = 0 . 275



    The experimental probability of choosing a watermelon candy is 0.275.

  4. probability = number   of   watermelon   candies total   number   of   trials = 135 400 = 27 80 = 0 . 338


    The experimental probability of choosing a watermelon candy is 0.338. The experimental probability of choosing a watermelon candy after 400 trials is closer to the theoretical probability than the experimental probability after 40 trials.

  5. The theoretical probability should be equal to the experimental probability when a large number of trials are performed.