Probabilities can be written in three equivalent forms: fractions, decimals or percentages. Each form describes the same likelihood, written in a different way. All forms must fit on the probability scale from zero to one.

 

 

Fractions

A probability written as a fraction shows the number of favourable outcomes compared to the total number of possible outcomes.

 

It is written as:

\( \frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes} \)

 

The fraction must:
• be greater than or equal to zero
• be less than or equal to one

 

For example, a probability of one half is written as:

\( \frac{1}{2} \)

 

Fractions are useful when outcomes can be counted exactly.

 

 

Decimals

A probability written as a decimal represents the same likelihood on the probability scale.

 

Decimal probabilities:
• lie between \( 0 \) and \( 1 \)
• are commonly used in calculations

 

For example, one half written as a decimal is:

\( 0.5 \)

 

Decimals make it easy to compare probabilities.

 

 

Percentages

A probability written as a percentage shows the chance out of one hundred.

 

Percentages:
• range from \( 0\% \) to \( 100\% \)
• are often used in everyday contexts

 

For example, one half written as a percentage is:

\( 50\% \)

 

Percentages must always be converted before being used in calculations.

 

 

Equivalence of Forms

Fractions, decimals and percentages can represent exactly the same probability.

 

For example, the following are equivalent:

\( \frac{1}{2} \)
\( 0.5 \)
\( 50\% \)

 

Only the format changes, not the likelihood.

 

Changing the form does not change the probability

 

 

Choosing an Appropriate Form

The most suitable form depends on context.

 

Fractions are useful when counting outcomes.
Decimals are useful for calculations.
Percentages are useful for communication and comparison.

 

You must be able to convert between all three forms accurately.

 

 

Common Errors to Avoid

Common mistakes include:
• giving probabilities greater than \( 1 \) or greater than \( 100\% \)
• forgetting to convert percentages correctly
• mixing forms without converting

 

Always check that probabilities lie within the correct range.

 

 

Key Points to Remember

Probabilities can be written as fractions, decimals or percentages.
All three forms represent the same likelihood.
Fractions compare favourable outcomes to total outcomes.
Decimals lie between \( 0 \) and \( 1 \).
Percentages lie between \( 0\% \) and \( 100\% \).

 

Being able to express probability in different forms allows likelihood to be communicated clearly and used correctly in calculations.