The probability scale
Use exact values between zero and one. Chance-band names here describe positions on that scale
- Impossible and certain In these finite models, zero is impossible and one is certain
- Even chance One half is equally likely to occur or not occur
- Convert first Percent means out of 100; “1 in n” means one divided by n
- Equal is not less Equivalent forms describe the same chance and cannot form a strict increasing pair
Worked example
Order these chances from lowest to highest
\[\begin{gathered}A:1\text{ in }5\\B:35\%\\C:\frac14\end{gathered}\]
- \(\displaystyle A=\frac15=0.2\)Convert one in five
- \(\displaystyle B=\frac{35}{100}=0.35\)Convert the percentage
- \(\displaystyle C=\frac14=0.25\)Convert the fraction
- \(\displaystyle 0.2<0.25<0.35\)Compare the exact values
- \(\displaystyle A<C<B\)Return to the original labels
Common mistakes
Comparing percent digits directly
✕\(\displaystyle 35\%>\frac12\)✓\(\displaystyle 0.35<0.5\)
35 percent is 35/100, not 35Treating equivalent forms as different chances
✕\(\displaystyle 0.5<\frac12\)✓\(\displaystyle 0.5=\frac12\)
Strict order requires genuinely different valuesTreating a small chance as impossible
✕\(\displaystyle 0.01=0\)✓\(\displaystyle 0<0.01<1\)
A small positive probability still allows the eventDifficulty levels
introIdentify all five chance bands, including boundaries
standardDistinguish likely and unlikely using mixed forms
challengeOrder five probability values in different forms
examOrder six values with boundaries; reject an option that repeats an equivalent value
Questions about this topic
What does “1 in 5” mean?+
It means a probability of one fifth. It does not guarantee a success in every set of five trials
Can a probability exceed one?+
No. One is the whole probability of the complete sample space
Is 0.99 certain?+
No. A one-percent chance of the complement remains
Can equivalent forms be strictly ordered?+
No. They are equal. A correct strict order cannot repeat one value using two spellings
Why convert before comparing?+
Different notations can make their sizes misleading. Compare the values using a common form
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 4: Probability
In this chapter
Describe and order probability valuesSingle-step theoretical probability and complements4A Probability scale and experiments: Experimental probability from observed frequenciesFinite events, probability assignments and complements4A Probability scale and experiments: Design and interpret a probability simulation4B Venn diagrams and sets: Venn regions, set language and probabilityCompound events, the addition rule and mutual exclusivityComplete and use a two-way probability tableConstruct and complete two-way frequency tablesConvert between Venn diagrams and two-way tablesConditional probability from exact representations4D Conditional probability: Conditional probability on Venn diagramsTwo-step sample-space tables with and without replacementRepresent a multi-stage finite sample spaceTree-diagram probability for two-stage experimentsMulti-stage probability, multiplication and total probability4G Independence and simulations: Independence on Venn diagramsTest exact independence4G Independence and simulations: Design and interpret a probability simulation4G Independence and simulations: Experimental probability from observed frequencies