D. Data · Data and Probability

Impossible, Possible, Certain: Events and Their Opposites

D2.1About 35 minutes

Learning goals

I can use the words impossible, possible and certain to describe how likely something is.
I can name the opposite (complementary) event, like "lands on red" and "does not land on red".
I can explain how likely an event and its opposite are.
I can use likelihood to make predictions and good decisions.

Words to know

likelihood
How likely something is to happen.

impossible
It can NOT happen.

possible
It MIGHT happen. Some possible things are more likely, some are less likely.

certain
It WILL happen for sure.

event
Something that might happen, like "the spinner lands on red".

complementary events
An event and its opposite, like "lands on red" and "does NOT land on red". One of the two will always happen.

more likely / less likely
Words to compare two possible events. "Likely" means it will probably happen. "Unlikely" means it probably will not happen, but it still could.

prediction
A smart guess about what will happen, using what you know.

Let's get started!

It is the first day of winter break. Will it snow today? Will you see a penguin in your backyard? Will tomorrow come after today?

Some things will happen, some things might happen, and some things can't happen at all!

Remember from Grade 1

Impossible: it will not happen. A moose will fly to the moon.
Possible: it might happen. It will snow in Ontario in December.
Certain: it will happen for sure. Tomorrow will come after today.

Possible things can be more likely or less likely.

The likelihood line. Possible covers everything between impossible and certain.

Events and their opposites

An event is something that might happen. Every event has an opposite: it happens, or it does not happen.

The spinner lands on red and the spinner does not land on red.
It snows tomorrow and it does not snow tomorrow.
The coin lands on heads and the coin does not land on heads (it lands on tails).

An event and its opposite are called complementary events. They fit together like two puzzle pieces: one of them will always happen.

How likely is the opposite?

If you know how likely an event is, you can figure out its opposite:

If an event is certain, its opposite is impossible.
If an event is impossible, its opposite is certain.
If an event is possible (but not certain), its opposite is possible too.
If an event is more likely, its opposite is less likely.

Event	Likelihood	Opposite event	Likelihood
The sun sets tonight	certain	The sun does not set tonight	impossible
A dog teaches our class	impossible	A dog does not teach our class	certain
It rains on Saturday	possible	It does not rain on Saturday	possible

Events and their opposites.

Spinners

Let's look at three spinners. Each one is cut into 4 equal parts.

Spinner A: all 4 parts are blue.

Spinner B: 2 red parts and 2 blue parts.

Spinner C: 3 red parts and 1 yellow part.

Worked example

Spinners and their opposites

For each spinner, how likely is landing on red? How likely is the opposite, not landing on red?

Spinner A has no red at all. Landing on red is impossible. So not landing on red is certain.
Spinner B has 2 red parts and 2 blue parts. Landing on red is possible. Not landing on red is possible too. They are equally likely, because there are the same number of red and blue parts.
Spinner C has 3 red parts and 1 yellow part. Landing on red is possible and more likely. Not landing on red (yellow) is possible but less likely.

A: red impossible, not red certain. B: both possible (equally likely). C: red more likely, not red less likely.

Worked example

Making a prediction

You will spin Spinner C one time. Predict: red or not red? Explain.

Both events are possible.
Red covers 3 of the 4 parts. Not red (yellow) covers only 1 part.
So red is more likely.

Predict red, because 3 of the 4 parts are red. Yellow could still happen, so we might be surprised!

Worked example

Rolling a number cube

A number cube has the numbers 1, 2, 3, 4, 5, 6. You roll it once. How likely is each event and its opposite?

Rolling a number less than 7
Rolling a 6

Every number on the cube is less than 7. So rolling less than 7 is certain. The opposite, rolling 7 or more, is impossible.
Rolling a 6 is possible. Only 1 of the 6 numbers is a 6, so it is less likely.
The opposite, not rolling a 6, means rolling 1, 2, 3, 4 or 5. That is 5 of the 6 numbers, so it is more likely.

Less than 7: certain (opposite impossible). Rolling a 6: possible, less likely (not rolling a 6 is more likely).

Just for fun

Likelihood, moose style: 🫎

Impossible: a moose flies to the moon.
Possible: a moose walks across a road in Algonquin Park.
Certain: the moose will either cross the road or not cross the road. An event and its opposite: one of them always happens!

Making good decisions

We use likelihood to make informed decisions:

Snow is likely tomorrow, so I will put my boots and snow pants by the door.
It is certain that it will get dark tonight, so I will bring my bike inside before supper.
It is impossible to swim in the frozen lake in January, so we will go skating instead, but only where a grown-up has checked that the ice is safe.

Hands-on activity

Spin and test

You need: a paper plate (or a circle drawn on paper), crayons, a pencil and a paper clip.

Divide your circle into 4 equal parts. Colour 3 parts red and 1 part blue.
Make a spinner: put the paper clip at the centre and hold it there with the pencil tip. Flick the paper clip.
Predict: Will it land on red or not red more often in 12 spins?
Spin 12 times. Tally red and not red.
Was your prediction right? Talk about it: "Red happened more because..."
Bonus: colour a new spinner so that landing on blue is impossible. What is certain on that spinner?

Your turn

What is the opposite of the event the coin lands on heads?

If an event is certain, how likely is its opposite?

A bag has only green counters. You pull one without looking. How likely is pulling green? Pulling not green?

A bag has 5 red counters and 5 blue counters. How likely is pulling red? Not red?

Is it impossible, possible or certain? It will snow somewhere in Canada this winter.

Spinner C has 3 red parts and 1 yellow part. Is landing on yellow more likely or less likely than not landing on yellow?

The weather report says rain is very likely this afternoon. What is a good decision?

More practice: warm-up

What does impossible mean?

What does certain mean?

Is it impossible, possible or certain? Your shoe will turn into a real dinosaur today.

Is it impossible, possible or certain? You will have pizza for supper tonight.

What is the opposite of the spinner lands on blue?

More practice: on your own

A spinner has 4 parts: blue, blue, blue, green. Which is more likely: landing on blue, or not landing on blue?

If it does not rain tomorrow is possible, how likely is it rains tomorrow?

You roll a number cube (1 to 6). Is rolling a 0 impossible, possible or certain? What about its opposite?

A jar has 8 orange and 2 purple marbles. Predict the colour you will pull. Explain.

Zoe says, "My spinner is half red and half blue, so landing on red is certain." Is she right?

Challenge

Design a spinner with 4 equal parts where landing on green is possible but not landing on green is more likely.

A bag has 3 yellow and 3 red blocks. You want pulling yellow to be certain. What could you do?

Snow is likely today, so not snowing is unlikely. Is not snowing impossible? Explain.

Check your understanding

Quiz

What is the opposite (complementary) event of the spinner lands on red?

If an event is impossible, its opposite is...

A spinner is all blue. Landing on blue is...

A spinner has 3 red parts and 1 yellow part. Which is more likely?

You roll a number cube with 1 to 6. Rolling a number less than 7 is...

Rain is likely today. What is the best decision?

For parents and teachers

What your child is learning: to use impossible, possible and certain to describe the likelihood of an event and its opposite (complementary events, such as "lands on red" and "does not land on red"), and to use likelihood to make predictions and decisions (Ontario expectation D2.1). We also use more likely, less likely and equally likely to compare possible events.

Key idea: one of the two complementary events always happens. If one is certain, the other is impossible; if one is possible (but not certain), so is the other.

Common difficulties:

Calling a very likely event certain, or an unlikely event impossible. Ask, "Could it possibly not happen?"
Thinking a prediction is wrong if the less likely thing happens. Explain that a good prediction can still be surprised.

At home: use the weather forecast, board game spinners and dice, or a bag of mixed socks. Ask, "How likely is it? How likely is the opposite? What should we do?"