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 chance in 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 means 35 out of 100, not 35.Treating 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 9 Mathematics, chapter 9: Probability and statistics
In this chapter
Finite events, probability assignments and complementsDescribe and order probability values9B Venn diagrams and tables: Venn diagrams, two-way tables and set notation for two eventsComplete and use a two-way probability tableCompound events, the addition rule and mutual exclusivity9C Set notation: Event notation and shaded regionsFinite sets and set operationsBuild two-step sample spaces with and without replacementUse two-step probability treesExperimental probability from observed frequenciesDesign and interpret a probability simulationFind the mean and the median, and choose between themWork backwards from a mean or medianMode, bimodal and no-mode data, and the effect of an outlierConstruct an ordered stem plot from raw dataConstruct and read back-to-back stem-and-leaf plotsDescribe the shape of a distributionGroup numerical data into class intervalsConstruct a histogram from a frequency tableRead values from a histogramFind the range, the quartiles and the IQRProduce a five-number summary and construct a boxplotRead values and percentages from a boxplotCompare a numerical variable across groupsSurveys and statistical investigations