Basic ProbabilityCambridge IGCSE Maths: Revision notes

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). Probabilities can be written as fractions, decimals or percentages.

• $P = 0$: the event cannot happen
• $P = 1$: the event is certain to happen
• $P = 0.5$: the event is equally likely to happen or not happen

For equally likely outcomes:

$P(\text{event}) = \frac{\text{number of favourable outcomes}}{\text{total number of possible outcomes}}$

Example: rolling a fair six-sided die, $P(\text{rolling a 4}) = \frac{1}{6}$.

Probabilities can be given as a fraction, decimal or percentage — always give the simplest equivalent form unless told otherwise.

The complement of an event is 'the event not happening'. Since all outcomes must add to 1:

$P(\text{event not occurring}) = 1 - P(\text{event occurring})$

Extended candidates use notation $P(A)$ for the event and $P(A')$ for its complement, so $P(A') = 1 - P(A)$.

• A fair object (coin, die, spinner) gives every outcome an equal chance
• A biased object does not give every outcome an equal chance — some outcomes are more likely than others
• A random process is one where the outcome cannot be predicted with certainty in advance

These words are commonly used in exam wording, so recognise them precisely: a 'biased die' means you cannot assume $\frac{1}{6}$ for each number.