Probability Scale - Measuring Likelihood from 0 to 1
The probability scale is a number line running from 0 to 1 that shows how likely any event is. Every probability sits somewhere on this scale. Learning to place events correctly on the scale – and to calculate exact values – is a core skill in probability.
The Scale
| Value | As a fraction | As a percentage | What it means |
|---|---|---|---|
| 0 | 0/1 | 0% | Impossible – cannot happen |
| 0.25 | 1/4 | 25% | Unlikely |
| 0.5 | 1/2 | 50% | Even chance (equally likely to happen or not) |
| 0.75 | 3/4 | 75% | Likely |
| 1 | 1/1 | 100% | Certain – will definitely happen |
Expressing Probability in Three Forms
A probability can always be expressed as a fraction, a decimal, or a percentage. All three are equivalent.
Example: P(even number on a die) = 3/6 = 1/2 = 0.5 = 50%.
Placing Events on the Scale
To place an event correctly:
- Calculate P(event) as a fraction.
- Convert to a decimal for easy placement on a 0–1 number line.
- Ask: is it closer to 0, to 0.5, or to 1?
Worked Examples
| Event | Fraction | Decimal | Position on scale |
|---|---|---|---|
| Rolling a 6 | 1/6 | 0.167 | Unlikely (close to 0) |
| Drawing a red card | 26/52 = 1/2 | 0.5 | Even chance |
| Number less than 7 | 6/6 = 1 | 1.0 | Certain |
Total = 10.
P(red) = 2/10 = 0.2 (unlikely).
P(blue) = 3/10 = 0.3 (unlikely but closer to even).
P(green) = 5/10 = 0.5 (even chance).
Check: 0.2 + 0.3 + 0.5 = 1.0 – all probabilities for one trial must sum to 1.
All Probabilities Must Sum to 1
When you list all possible outcomes of an experiment, the sum of their probabilities must equal exactly 1. This is a powerful check – if your probabilities do not add to 1, you have made an error.
Key Takeaways
- Probability is always between 0 (impossible) and 1 (certain), inclusive.
- Probability can be expressed as a fraction, decimal, or percentage – all equivalent.
- The probabilities of all outcomes of an experiment sum to exactly 1.
- 0.5 = even chance; below 0.5 = unlikely; above 0.5 = likely.
Practice Questions
- A spinner has 8 equal sections (3 red, 2 blue, 3 green). Find P(red), P(blue), P(green) and confirm they sum to 1.
- Place P(0.1), P(0.5), P(0.9) on a probability scale and describe each as impossible/unlikely/even/likely/certain.
- A die is rolled. Write all six probabilities and confirm they sum to 1.
- P(A) = 0.42, P(B) = 0.35. If A and B are the only two possible outcomes, do they sum to 1? What is missing?
- Convert P = 3/8 to a decimal and a percentage, then describe its position on the scale.