The probabilty of an **event** occurring is given by:

probability = `frac(text(outcomes))(text(total))`

where **outcomes** is the number of times an outcome can occur, and the total is the total of all possible outcomes. For example, an even number can happen `frac(3)(6)` when a dice is thrown.

A probability is written as **P**(event) = *value*. The probability of an even number from a dice throw is written as **P**(even number)=`frac(1)(2)`.

The probability of an event NOT happening + the probability of an event happening = 1, as the probability of an event happening plus the probability of an event *not* happening is certain.

**P**(event) + **P**(not event) = 1

What is the probability of selecting, at random, a red ball from a bag that contains 5 red balls, 7 blue balls, 9 green balls and 9 white balls?

There are 5 red balls that could be selected.

There are 30 balls altogether.

The probability of selecting a red ball is `frac(5)(30)` = `frac(1)(6)`

Answer: **P**(red ball) = `frac(1)(6)`

What is the probability of not throwing a prime number with an eighteen-sided die (dice)?

There are a total of 18 ways of throwing any number.

Prime numbers up to 18 are 2, 3, 5, 7, 11, 13, 17. There are 7 ways of throwing a prime number.

**P**(prime) = `frac(7)(18)`

**P**(not prime) = 1 - `frac(7)(18)` = `frac(11)(18)`

Answer: **P**(not prime) = `frac(11)(18)`

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).