These questions ask you to place an event on the probability scale, choose the matching word, or compare two chances. Treat the number as a position from never happening to always happening.
Locate the chance before naming it
The endpoints have exact meanings: 0 is impossible and 1 is certain. Halfway between them is 0.5, and this is an even chance. A probability strictly between 0 and 0.5 is unlikely; one strictly between 0.5 and 1 is likely. The words describe regions of the scale, while impossible and certain belong only to the endpoints.
| Position on the scale | Description |
|---|---|
| Exactly 0 | Impossible |
| Above 0 but below 0.5 | Unlikely, but still possible |
| Exactly 0.5 | Even chance |
| Above 0.5 but below 1 | Likely, but not certain |
| Exactly 1 | Certain |
For equally likely outcomes, count favourable outcomes out of all outcomes. A fair spinner with six equal sections, four marked with a star, gives a star probability of 4/6. That fraction is above halfway but below 1, so the event is likely rather than certain. To compare decimals, use place value; to compare unit fractions, remember that cutting the same whole into more equal parts makes each part smaller.
Where mistakes come from
| Tempting route | How to reject it |
|---|---|
| Write the number of successful outcomes, or 100, for certainty | Counts and percentages use different units. On this probability scale, an event covering every outcome has value 1. |
| Use the number of possible results as the probability of one result | Probability is favourable outcomes divided by all equally likely outcomes, so it cannot exceed 1. |
| Call a rare event impossible | Any positive probability shows that the event can happen. Only exactly 0 marks an impossible event. |
| Treat the denominator alone as the size of a unit fraction | For unit fractions, a larger denominator gives a smaller piece of the same whole. |
Try it
A bag holds 9 red counters and 1 blue counter, and one counter is taken at random. Select all statements that are true about taking a red counter. Select all that apply.
- Taking a red counter is certain, because most of the counters are red
- Taking a red counter is likely
- The probability of red is 9 out of 1, one red counter for each blue counter
- The probability of red is 9 out of 10
- Taking a red counter is not certain, because the bag still holds a blue counter
A fair spinner has 8 equal sections, of which 7 are shaded. Which word describes landing on a shaded section, and what is its probability as a fraction out of the total number of sections?
- Likely, with probability 7/8
- Likely, with probability 1/8
- Certain, with probability 8/8
- Likely, with probability 7
A pupil writing about the probability scale says that 0.4, 1.2 and 0 can all be probabilities. Which one of the three numbers cannot be a probability?
- 1.2
- 0
- 0.4
- None of them, all three are possible probabilities