ACARA v9 CONTENT DESCRIPTION “recognise that probabilities lie on numerical scales of 0 - 1 or 0% - 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals”
Builds on: Numbers Beyond 10 000 (AC9M3N01). Placing a chance on a 0 to 1 scale uses the same number-line sense as locating any number — here the line runs from impossible to certain.
Chance lives on a scale
Every chance can be placed on a single scale that runs from 0 to 1. A probability of 0 means the event is impossible, a probability of 1 means it is certain, and everything else sits in between: the closer to 1, the more likely. The same scale can be written 0 to 100 percent, with one half landing at 50 percent. Nothing real has a probability below 0 or above 1, which is why a value like 1.4 can be ruled out at a glance. This unit places events on that scale and estimates where each one belongs.
The scale from 0 to 1
Every probability lives on a scale from impossible to certain. Place each event.
The sun rises tomorrow: about 100% likely — every probability sits somewhere from 0 (impossible) to 1 (certain).
One chance, three notations
A probability can be written as a fraction, a decimal or a percentage, and the three are just different clothes for the same number. A coin landing heads is one half, 0.5, or 50 percent; all three name the same point on the scale. Being able to move between the forms matters because some chances are clearest as fractions, like one in six for a die, while others read best as percentages, like a 30 percent chance of rain. Recognising that a fraction, a decimal and a percentage can describe one chance keeps the scale easy to use.
Fraction, decimal or percentage
One chance, three notations. The same likelihood wears all three.
1/2, 0.5 and 50% are the same chance — a probability can be written as a fraction, a decimal or a percentage.
Counting equally likely outcomes
When every outcome of a situation is equally likely, a probability can be counted directly: it is the number of favourable outcomes out of the total. A die has six equally likely faces, so the chance of a 6 is one out of six; the chance of an even number is three out of six, because three faces are even. This counting gives exact probabilities for coins, dice and spinners, and it anchors the scale — a fair coin sits exactly at one half because one of its two equally likely sides is heads.
Counting equally likely outcomes
When every outcome is equally likely, the probability is the favourable share of them.
a coin landing heads: 1 of the 2 equally likely outcomes count, a probability of 1/2.
Estimating a chance
Not every event can be counted so neatly, and many everyday chances are estimated instead. Will it rain on a clear summer day? Unlikely, so low on the scale. Will a tossed coin land tails? An even chance, right in the middle. Estimating means judging roughly where an event falls — unlikely, even, or likely — and then refining that into a fraction, decimal or percentage. Good estimates come from the context: what you know about the situation guides where on the 0 to 1 scale the chance belongs.
Estimating a chance
Place an everyday event in the unlikely, even or likely zone of the scale.
A coin lands tails. Is it unlikely, even or likely?
The chance it does not happen
Every event has an opposite: the chance it does not happen. Because the event either happens or it does not, these two chances always add to the whole, to 1 or to 100 percent. If rain has a 30 percent chance, then no rain has 70 percent; if a die has a one in six chance of a 6, the chance of not a 6 is five in six. This is often the quickest route to an answer, since the chance of something not happening can be easier to find than the chance that it does.
The chance it does not happen
An event and its opposite fill the whole scale. Together they make 100 percent.
If rain has a 30% chance, then not rain has 70% — the two always add to 100%.
Fixed points on the scale
A few chances anchor the whole scale and are worth knowing by heart. Impossible is 0; certain is 1; a perfectly even chance, like a fair coin, is one half, or 50 percent. Every other probability is read against these landmarks: a likely event sits between one half and 1, an unlikely one between 0 and one half. Matching a described chance to its value on the scale, and ruling out impossible values above 1 or below 0, is the core skill that the rest of probability is built upon.
Match the chance to a value
Impossible, certain and even map to fixed points on the 0 to 1 scale.
An impossible event has a probability of... Pick A, B or C.
From estimates to experiments
With the 0 to 1 scale, the three notations, and the idea of equally likely outcomes, any chance can be described, estimated and placed. These are the foundations on which the rest of probability rests: from here the same scale carries repeated experiments and simulations, where many trials are run and the results are compared against these estimated chances to see how closely observation matches expectation.
Quick self-check
1. On the probability scale, an event that is certain to happen has a value of...
2. A coin is tossed. The probability it lands heads is closest to...
3. Which probability could NOT be correct for any event?
4. A die is rolled. The probability of getting a 6 is about...
5. If the chance of rain is 30%, the chance of no rain is...