Order chance words on a 0-1 scale
Theory
The chance of an event can be placed on a scale from 0 (impossible) to 1 (certain). The halfway point \(\dfrac{1}{2}\) is an even chance; unlikely events sit below it and likely events sit above it.
A probability measures how likely an event is, as a number from \(0\) to \(1\).
Impossible events have probability \(0\); certain events have probability \(1\).
An even chance is exactly \(\dfrac{1}{2}\) — the event is just as likely to happen as not. Unlikely sits between \(0\) and \(\dfrac{1}{2}\); likely sits between \(\dfrac{1}{2}\) and \(1\).
Each chance word matches a place on the \(0\) to \(1\) scale.
| Chance word | Where on the scale |
|---|---|
| impossible | \(0\) |
| unlikely | between \(0\) and \(\dfrac{1}{2}\) |
| even chance | \(\dfrac{1}{2}\) |
| likely | between \(\dfrac{1}{2}\) and \(1\) |
| certain | \(1\) |
How to order events by chance
- Judge each event: can it never happen \((0)\), always happen \((1)\), or somewhere between?
- Compare the in-between events to an even chance \(\left(\dfrac{1}{2}\right)\).
- Read the scale from left to right to list them from least to most likely.
A die only shows \(1\) to \(6\), so a \(7\) can never come up.
| \(P(\text{roll a }7)\) | \(=\) | \(0\) |
It sits at the very start of the scale.
A head and a tail have the same chance.
| \(P(\text{head})\) | \(=\) | \(\dfrac{1}{2}\) |
This is an even chance, halfway along the scale.
Die \(6\) is \(\dfrac{1}{6}\); tails is \(\dfrac{1}{2}\); less than \(7\) is certain \((1)\).
Order: die \(6\), coin tails, die \(<7\).
Start at \(0\), finish at \(1\), even chance in the middle:
impossible, unlikely, even chance, likely, certain.
Common pitfalls
Frequently asked questions
What does a probability of 0 mean?
It means the event is impossible — it can never happen, like rolling a \(7\) on an ordinary \(6\)-sided die.
What is an even chance?
An even chance is a probability of \(\dfrac{1}{2}\). The event is just as likely to happen as not, like a fair coin landing on heads.
What is the difference between unlikely and impossible?
Impossible means it can never happen \((0)\). Unlikely means it can happen but probably will not; it sits between \(0\) and \(\dfrac{1}{2}\).
Can a probability be more than 1?
No. Every probability is between \(0\) and \(1\). Nothing can be more likely than certain, and certain is \(1\).