D. Data · Data and Probability

Impossible, Unlikely, Equally Likely, Likely, Certain

D2.1About 40 minutes

Learning goals

I can use the words impossible, unlikely, equally likely, likely and certain to describe events.
I can tell how likely a spinner or a bag is to give each result.
I can use likelihood to make predictions and good decisions.

Words to know

event
Something that might happen, like spinning green or rolling a 6.

likelihood
How likely something is to happen.

impossible
It cannot happen.

unlikely
It could happen, but probably will not.

equally likely
Two events have the same chance of happening.

likely
It will probably happen, but it is not for sure.

certain
It will happen for sure.

prediction
A thoughtful guess about what will happen, based on what you know.

Remember from Grade 2

You described events as impossible, possible or certain, and you learned that every event has an opposite (spinning green and not spinning green). In Grade 3 we split possible into more exact words: unlikely, equally likely and likely.

A likelihood line

We can put events on a line, from impossible to certain.

Likelihood line: impossible, unlikely, equally likely, likely, certain.

Word	Meaning	Example
Impossible	Cannot happen	A number cube with 1 to 6 lands on 7.
Unlikely	Could happen, but probably won't	Picking the one yellow block from a bag of 9 green blocks and 1 yellow block.
Equally likely	Same chance	A coin lands heads or tails.
Likely	Will probably happen	Picking a green block from that same bag.
Certain	Will happen for sure	Tomorrow comes after today.

The five likelihood words.

Spinners

On a spinner, a bigger part means the arrow is more likely to stop there. Parts that are the same size are equally likely.

Spinner A has 4 equal parts. 3 are green and 1 is yellow.

Spinner A: 4 equal parts. 3 parts are green and 1 part is yellow. There is no blue.

Worked example

Example 1: Describe Spinner A

Use likelihood words to describe spinning green, yellow, blue, and green or yellow on Spinner A.

Green covers 3 of the 4 equal parts, more than half. Green is likely.
Yellow covers only 1 of the 4 parts. Yellow is unlikely.
There is no blue on the spinner. Blue is impossible.
Green or yellow: every part is green or yellow, so the arrow must stop on one. It is certain.

Green: likely. Yellow: unlikely. Blue: impossible. Green or yellow: certain.

Spinner B: 4 equal parts. 2 parts are green and 2 parts are blue.

Worked example

Example 2: Equally likely

On Spinner B, is green or blue more likely?

Green has 2 equal parts.
Blue has 2 equal parts.
They cover the same amount of the spinner.

Green and blue are equally likely. If you spin many times, you'd expect about the same number of each.

Bags of blocks

Likelihood works for bags too. If you reach in without looking, the colour with more blocks is more likely.

🟩🟩🟩🟩🟩🟩🟨🟨

A bag with 6 green blocks and 2 yellow blocks.

Worked example

Example 3: Make a prediction

Ella picks a block from the bag without looking, writes down the colour and puts it back. She does this 16 times. Predict: will she get more green or more yellow?

There are 6 green and 2 yellow. Green is likely, yellow is unlikely.
Green blocks are 3 times as many as yellow (6 is 2 + 2 + 2).
So she will probably get more green, maybe about 12 green and 4 yellow.

Prediction: more green than yellow. It won't be exact every time, because it is chance, but green should come up much more often.

Worked example

Example 4: An informed decision

In a game, you win if the spinner lands on green. You may choose Spinner A or Spinner B. Which should you choose?

Spinner A: green is 3 of 4 parts.
Spinner B: green is 2 of 4 parts.
Green is more likely on Spinner A.

Choose Spinner A. That's an informed decision: you used likelihood to choose.

Likely is not certain!

A likely event can still not happen, and an unlikely event can still happen. On Spinner A, you could spin yellow twice in a row. That's chance! Likelihood tells us what will probably happen, especially over many tries.

Spinner C: half of the spinner is yellow, one quarter is green and one quarter is blue. You will use it in the practice.

Just for fun

Will a cow jump over the moon tonight? Impossible! Unless you are reading the nursery rhyme. Then it is certain!

Hands-on activity

Make and test a spinner

You need: paper, a pencil, crayons, a paper clip and a sharpened pencil.

Draw a circle (trace around a cup). Divide it into 4 equal parts, like a pizza cut in 4.
Colour 3 parts one colour and 1 part another colour.
To spin: put the pencil tip through the paper clip at the centre of the circle, hold the pencil straight up, and flick the paper clip. (A grown-up should help with the sharp pencil tip.)
Predict which colour will come up more in 20 spins.
Spin 20 times and tally the results in a frequency table.
Was your prediction right? Talk about why the results were not exactly 15 and 5.

Your turn

Spinner A (3 green parts, 1 yellow part): how likely is spinning green?

Spinner A: how likely is spinning yellow?

Spinner A: how likely is spinning blue?

Spinner B (2 green parts, 2 blue parts): compare green and blue.

You flip a coin. How likely is heads, compared with tails?

You roll a number cube with the numbers 1 to 6. How likely is it to land on 7?

Tomorrow, the sun will rise. Which word fits?

More practice: warm-up

Which word means it cannot happen?

Which word means it will happen for sure?

Which word means it could happen, but probably won't?

On a spinner, does a bigger part make that colour more likely or less likely?

A bag has 5 green blocks and 5 yellow blocks. Is green or yellow more likely?

More practice: on your own

Look at Spinner C (half yellow, one quarter green, one quarter blue). Which colour is most likely? Which two colours are equally likely?

You roll a number cube (1 to 6). Is rolling a number less than 7 impossible, unlikely, likely or certain?

You roll a number cube (1 to 6). Is rolling a 6 likely or unlikely? Explain.

A bag has 2 green blocks and 8 yellow blocks. Describe picking green, then picking yellow.

You want to pick a yellow block. Bag 1 has 6 green and 2 yellow. Bag 2 has 2 green and 8 yellow. Which bag do you choose? Why?

Challenge

Design a spinner with 4 equal parts where yellow is likely, blue is unlikely and green is impossible.

Predict: if you spin Spinner A 40 times, about how many times will it land on green? Explain.

Max and Lia play a game with Spinner C. Max gets a point for yellow. Lia gets a point for green or blue. Is the game fair? Explain.

Check your understanding

Quiz

A spinner has no blue parts. Spinning blue is...

Spinner A has 3 green parts and 1 yellow part, all the same size. Spinning green is...

A coin landing on heads or on tails is...

A bag has 9 green blocks and 1 yellow block. Picking yellow without looking is...

You win on green. Spinner A has 3 green parts out of 4. Spinner B has 2 green parts out of 4. Which should you choose?

Rolling a number less than 7 on a number cube with the numbers 1 to 6 is...

For parents and teachers

What your child is learning: to use the words impossible, unlikely, equally likely, likely and certain to describe events, and to use likelihood to make predictions and informed decisions (Ontario expectation D2.1). In Grade 2, children used impossible, possible and certain.

Common difficulties:

Treating likely as certain. A likely event can still not happen, and an unlikely one can happen.
Thinking the result of the last spin changes the next one ("Yellow is due!"). Each spin is a fresh start.
Comparing spinners by counting parts that are not the same size. Size of the part matters.
Expecting an experiment to match the prediction exactly. Results come out close, especially with many tries, but rarely exact.

At home: play games with dice, spinners or coins and talk about likelihood: "Is rolling a 6 likely or unlikely? What about rolling an even number?" Supervise small objects like dice, coins and paper clips around younger children, and help with the sharp pencil in the spinner activity.