Understand the idea.
Impossible and certain
Use impossible when the setup gives no way for an event to happen. Choosing green from a bag containing only red and blue counters is impossible. Use certain when every possible choice makes the event happen.
From that bag, choosing red or blue is certain because those are all the available colours. Always describe the actual setup: what happened before, or what you hope will happen, cannot make another result certain.
Likely is not promised
When same-sized counters are well mixed and chosen without looking, more counters of a colour give more chances to choose it. Five red and two blue make red more likely than blue, but either colour can appear.
Likely does not mean certain, and unlikely does not mean impossible. With a fair coin landing on a flat face, heads and tails are equally likely: neither face has a better chance and neither is guaranteed.
See the method in action.
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?
Worked solution
- 1
Compare the colour counts.
There are five red counters and only two blue counters.
- 2
Use the stated choosing conditions.
Same-sized counters, good mixing and choosing without looking give each counter the same chance of being picked. More counters therefore favour red.
- 3
Keep blue among the possible results.
Blue counters are still in the bag, so red is more likely but blue is still possible.
Red is more likely, but blue is still possible.
Two chance words
A cup contains only yellow counters. Describe choosing yellow and choosing black.
Worked solution
- 1
Consider choosing yellow.
Every counter in the cup is yellow, so whichever counter is chosen will be yellow. Yellow is certain.
- 2
Consider choosing black.
There is no black counter available to choose, so black is impossible.
Yellow is certain; black is impossible.
Try it yourself.
Check your understanding
A mixed bag contains nine blue counters and one red counter. Is red impossible or unlikely?
Show answer & reasoning
Unlikely.
There is one red counter available, so red is possible. With nine blue counters and only one red, choosing red is unlikely, rather than impossible.
Keep practising
6 worksheet questions
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 ↗