Minds On

Let’s play!

Let’s play a game called “Let’s Play!.” To play you will need two dice or you can use a digital tool or you can consider the possible outcomes based on the rules.

The rules of the game are as follows:

  • Roll the digital dice.
  • Multiply the two numbers
  • If the product is even, earn 1 point.
  • If the product is not even, continue to play.
  • Continue for 30 trials
  • Record how many times you earned a point.

Reflect

Reflect on the game by answering these questions.

  • Is this a fair game? Why or why not? Explain your thoughts.
  • Suppose you tallied up (calculated) 60 trials. Would this help you decide if the game was fair or not?
  • If the game is unfair, how could you modify the rules to make it a fair game?
  • Throughout this learning activity, record your thoughts digitally, orally, or in print.

Action

Explore this experimental probability

Experimental probability is defined as the measurement of the likelihood of an event happening, based on performing an experiment.

For example, imagine a number cube labelled 1-6 was rolled, or a button was pressed which shares the outcome out loud and in written form. Check the results in the relative frequency table below.

Result Tally Frequency Relative Frequency

Even numbers

15

15/34

Odd numbers

19

19/34

The experimental probability of getting an even number is 15/34 and the experimental probability of getting an odd number is 19/34.

Experimenting

Imagine there are 4 outcomes for a particular experiment: A, B, C and D.

Each of the outcomes has an equal chance of occurring.

Question 1

From Learning Activity 10, you know that Theoretical probability is the mathematical calculation of the chances that an event will happen in theory. If all outcomes are equally likely, it is calculated as the number of favourable outcomes divided by the total number of possible outcomes.

  • What is the theoretical probability of any of the options occurring?
  • If you were to conduct 20 trials, how many times would you expect a particular outcome to occur? For example, how many times would you expect to get an A?

Use a spinner (paper or digital) with the four options on it, or flash cards with the options written on the cards, and shared out loud, or another four-option grouping. Conduct 20 trials and record your results in the Relative Frequency Table in your notebook or using the following fillable activity document. You can also use another graphic organizer, or an audio recording.

Result Frequency Tally Relative Frequency

Option A

Option B

Option C

Option D

Press the ‘Activity’ button to access the Relative Frequency Table. 

Activity(Open PDF in a new window)

Using the information:

  • Repeat the experiment another 20 times. Record your results in the same frequency table you used before. What do you notice?
  • If you were to do the experiment another 20 times, what do you think you might start to notice?
  • Compare your own individual experimental probability results to your predicted results from the first part of Question 1. What do you notice?
  • Based on what you notice (each time), how many times should the experiment be repeated? Can you make any conclusions based on what happens when you try an experiment more often?
  • Reflect on what you have learned about the effect of repeating experiments. How might this affect how you play a board game with family or friends?

Consolidation

Design your own experiment

Imagine you were told that the theoretical probability of winning a game is 1/2. You play the game 10 times and find the experimental probability is 2/10.

  • Why do you think the experimental probability is so different than the theoretical probability?
  • Design a probability experiment of your own. The experiment should have 1/2 a chance of winning.
  • Conduct the experiment 10 times and record the results. Were they what you expected?
  • What could you do to have the experimental results more closely approach the theoretical probability of winning?

Think about your learning

Answer the following questions to reflect on your learning. You can record your responses using a method of your choice.

  • Explain the difference between theoretical and experimental probability.
  • What can you do to increase the chances that the experimental probability will not match the theoretical probability?
  • What can you do to decrease the chances that the experimental probability will not match the theoretical probability?
  • When might someone want to increase or decrease the chances that the experimental probability will not match the theoretical probability?

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel…

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.

Create individual slips of paper or flash cards and label them from 1 to 30.

Shuffle the cards. Select one card and record the result. Return the card into the pile and shuffle again.

  • If you turn an odd number, you get 1 point. If you turn a number that is a multiple of 4 then you do not get any points. Make sure you return the slip of paper or flash card to the pile after each selection and shuffle before you begin again.
  • Predict the possible outcome after 10 trials; how many points might you earn? Justify your answer using theoretical probability.
  • Now, play the game 10 times. Did your results match your prediction? Why or why not?