The idea, step by step
Impossible and certain
An impossible event cannot happen in the setup. Choosing green is impossible from a bag containing only red and blue counters. A certain event must happen: the chosen counter will be red or blue.
Always name the setup. Rain tomorrow is not certain just because it rained today. Our experience may help us predict, but a prediction is not a guarantee.
Likely is not promised
When same-sized counters are well mixed, a colour with many counters is more likely to be chosen than a colour with only a few. In this bag, red is likely and blue is unlikely.
Blue can still be chosen. If a fair coin has equally likely flat faces, neither heads nor tails is favoured. Neither result is certain.
A common trap
An unlikely event cannot happen.
Instead: Unlikely means there is a small chance, not no chance. Impossible means it cannot happen in the stated setup.
See the thinking
Compare the colours
Use the bag of five red and two blue same-sized counters. Which colour is more likely when the bag is mixed and we choose without looking?
- There are more red counters than blue counters.
- The counters are the same size and are well mixed.
- There are more chances to choose red.
Two chance words
A cup contains only yellow counters. Describe choosing yellow and choosing black.
- Every available counter is yellow.
- There are no black counters to choose.
Check your understanding
A mixed bag contains nine blue counters and one red counter. Is red impossible or unlikely?
Show answer
Unlikely.
A red counter is present, so choosing it is possible.
Your turn
6 questions · Work at your own pace.
Read the questions online
- A bag contains only orange counters. Describe choosing orange using a chance word.
- The same bag has no white counters. Describe choosing white.
- A mixed bag has 8 green and 2 yellow same-sized counters. Which colour is more likely?
- Could yellow still be chosen from a bag of 8 green and 2 yellow counters? Explain.
- An ordinary fair coin lands on a flat face. Is heads certain? Explain.
- A mixed bag has 4 red and 4 blue same-sized counters. Is either colour more likely? Explain.
Read the worked solutions
- A bag contains only orange counters. Describe choosing orange using a chance word.
Every available counter is orange.
Certain. - The same bag has no white counters. Describe choosing white.
No white counter is available.
Impossible. - A mixed bag has 8 green and 2 yellow same-sized counters. Which colour is more likely?
There are more green counters: 8 compared with 2.
Green. - Could yellow still be chosen from a bag of 8 green and 2 yellow counters? Explain.
Two yellow counters are present.
Yes. Yellow is less likely than green, but it is possible. - An ordinary fair coin lands on a flat face. Is heads certain? Explain.
The setup has two possible flat-face results.
No. Tails is also possible and equally likely. - A mixed bag has 4 red and 4 blue same-sized counters. Is either colour more likely? Explain.
There are equal numbers under the same choosing conditions.
No. The colours are equally likely.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Curriculum
Possible outcomes; likely/unlikely/certain/impossible; repeated experiments; variation.
Official curriculum source ↗