Minds On

Probability

Review the concept of probability with Professor P and Lady Vocab. As you explore the video, keep track of the mathematical vocabulary used.

Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

Some of the key words from the video are outcome, likely, unlikely, and chance. Make sure that you have recorded your definitions for these terms.

Think of…

Consider the following:

  • Think of something that is unlikely to happen.
  • Think of something that is certain to occur.
  • Think of something that will never happen.
  • Think of something that is likely to happen.

What is the difference between something that is likely to happen and something that is certain to happen?

What is the difference between something that is unlikely to happen and something that will never happen?

What is the difference between something that is likely to happen and something that is unlikely to happen?

Record your responses using a method of your choice.

Likely, unlikely, certain, or never?

Decide if the event will never happen, is unlikely to happen, likely to happen, or certain to happen. Explain your thoughts. Record your responses using a method of your choice.

Select the correct answer.

Action

Time to review a few terms

Probability is a number from 0 to 1 that shows how likely it is that an event will happen.

An event is the outcome of a specific incident or situation being tracked in an experiment.

Outcomes are possible results of an experiment. For example, two sports teams playing against each other, they can tie, or one team will win and the other will lose.

A probability line is a line with 0 at the left end (for “impossible”) and 1 at the right end (for “certain”). Probabilities for events can be plotted on the line to show how these probabilities relate to each other.
A probability with 0 “impossible” at one end and 1 “certain” at the other end. Other probabilities are plotted in between.

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.

For example, suppose a class cannot decide between playing basketball or lacrosse. The Physical Education teacher understands probability, so the teacher mentions to the class:

“We seem to be unable to decide. A fair method to decide is tossing a coin. Heads could represent basketball and tails could represent lacrosse.

The number of outcomes for basketball only is 1 and the number of outcomes for lacrosse only is 1. The total number of outcomes is 2. Therefore, the theoretical probability of basketball being selected is ½. The theoretical probability of lacrosse being selected is also ½.”

Favourable outcomes are the outcomes that you are hoping occurs.

So, if the theoretical probability is represented as a fraction, it can be represented as:

Determine the probability of events tasks

Task 1

Imagine you have a spinner divided into four sections, or a button which produces the same four different options at random. Each section is divided equally on the spinner and has an equal chance of being selected when pressing the button.

The sections are labelled as Bear, Rabbit, Elephant, Giraffe.

Alternatively, you can check theSpinner.

Press the ‘Activity’ button to access Spinner. 

Activity(Open PDF in a new window)

Next, decide:

  • How many outcomes does the button/spinner have?
  • How many of these outcomes are Bear?
  • If the Rabbit section is the favourable outcome, then what is the theoretical probability of selecting a Rabbit? Express this as a fraction.
  • If Bear and Elephant are the favourable outcomes, then what is the theoretical probability of selecting Bear or Elephant? Express this as a fraction.
  • What is the theoretical probability of selecting Rabbit or Giraffe? Express this as a fraction.

Press ‘Answer’ to reveal the solution.

  1. The spinner/button has 4 outcomes.
  2. Bear is 1 outcome.
  3. If Rabbit is the favourable outcome, the theoretical probability of selecting a Rabbit is 1 4
  4. If Bear and Elephant are the favourable outcomes, then the theoretical probability of selecting a Bear or an Elephant is 2 4 or 1 2
  5. The theoretical probability of selecting Rabbit or Giraffe is 2 4 or 1 2

Task 2

Imagine you are selecting from a stack of cards labelled with different items. Written on each card is one item. In the stack there are one marble, one rock, one eraser and two paper clip cards. At each turn, the partners can observe what is written on the card as well as share out loud. Each of these items can be selected at each turn. Therefore, there are always five cards available to select.

Alternatively, check the following Stack of Cards document.

Press the ‘Activity’ button to access Stack of Cards. 

Activity(Open PDF in a new window)

Calculate the theoretical probability of the following events and express each event as a fraction. Record your responses using a method of your choice.

  • Having a marble selected.
  • Having a rock selected.
  • Having an eraser selected.
  • Having a paper clip selected.
  • Which is a likelier event, selecting either a marble or rock, or selecting either a paper clip or rock? How do you know? Explain your thinking.

Press ‘Answer’ to reveal the solution.

  1. The theoretical probability of selecting a marble would be 1 5
  2. The theoretical probability of selecting a rock would be 1 5
  3. The theoretical probability of selecting an eraser would be 1 5
  4. The theoretical probability of selecting a paper clip would be 2 5
  5. Selecting either a paper clip or rock is a likelier event than selecting either a marble or rock because you have a 3 5 chance to select a paper clip or a rock but only a 2 5 chance to select a marble or a rock. 3 5 > 2 5

Task 3

Imagine a button is pressed and a number from one to six is revealed. Calculate the theoretical probability for each of the following statements and express it as a fraction. Record your answers using a method of your choice.

An image of a number cube with 6 faces. Each face has a number from 1 to 6.
  • Probability of getting an odd number.
  • Probability of getting an even number.
  • Probability of getting a number less than seven.
  • Probability of getting a number greater than two.

Press ‘Answer’ to reveal the solution.

  1. Probability of getting an odd number- (1, 3, 5) so 3 6 or 1 2
  2. Probability of getting an even number- (2, 4, 6) so 3 6 or 1 2
  3. Probability of getting a number less than 7. All numbers so 6 6 or 1
  4. Probability of getting a number greater than 2. (3, 4, 5, 6) so 4 6 or 2 3

Task 4

Examine the probability line below.

A probability line with arrows from left to right that read: never, unlikely, equally likely, likely, and certain.

Using the language of probability, explain and identify two events that are:

  • equally likely to happen
  • unlikely to happen
  • likely to happen

Use a method of your choice to record your responses.

Consolidation

Task 1: Probability devices

Design or describe a probability device (e.g., a spinner, flash cards, digital device) that matches the following probabilities:

  • 1/2
  • 2/3
  • 5/8
  • 3/5

Task 2: What is the Probability?

For each event, select the corresponding probability. Alternatively, record your responses using a method of your choice.

Task 3: Think about your learning

Image is decorative so no alt is needed.

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

Theoretical probability is what we expect to happen, and experimental probability is what happens when we try something out.

  • Think of a time the theoretical probability matched what happened. Why do you think it worked out that way? If you cannot come up with an example, do some research to find an example.
  • Think of a time the theoretical probability did not match what happened. Why do you think it worked out that way? If you cannot come up with an example, do some research to find an example.

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.

Design a Scenario

Design two situations that have a probability of 3/4. Record your answers using a method of your choice.

Predict what will happen next (optional)

The following data was collected comparing two events after 15 trials:

Flip Result
1 Heads (H)
2 Tails (T)
3 H
4 H
5 T
6 H
7 H
8 T
9 H
10 H
11 T
12 H
13 H
14 T
15 H
Two sides of a coin. One side is heads and the other is tails.

What do you think will happen on the 16th trial? Explain your thinking.