Basic ProbabilityEdexcel GCSE Maths: Revision notes

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). It can be written as a fraction, decimal or percentage.

Probabilities can never be negative or greater than 1.

When all outcomes of an experiment are equally likely (each just as likely as any other), the probability of a specific event is:

P(event) = number of favourable outcomes ÷ total number of possible outcomes

This assumes randomness and fairness — for example, a fair coin or an unbiased die. From a probability, you can calculate the expected number of successes in n trials: expected number = probability × n.

Example: rolling a fair die, P(rolling a 6) = 1/6. In 60 rolls, the expected number of 6s = (1/6) × 60 = 10.

Theoretical probability is calculated using known facts about equally likely outcomes (e.g. 1/6 for a die). Relative frequency (experimental probability) is calculated from actual results of an experiment:

relative frequency = number of times an event occurs ÷ total number of trials

Relative frequency is only an estimate of the true probability, but the more trials carried out, the closer the relative frequency tends to get to the theoretical probability — larger samples give better estimates.

For any exhaustive set of outcomes (an outcome from the set must happen), the probabilities of all the outcomes add up to exactly 1.

This is especially useful for mutually exclusive events (events that cannot happen at the same time) — if you know the probability of an event happening, the probability of it NOT happening is 1 minus that probability.

Example: P(rain tomorrow) = 0.3, so P(no rain tomorrow) = 1 − 0.3 = 0.7.

A two-way table organises data or outcomes by two categories at once (rows and columns), making it easy to read off probabilities directly.

To find a probability from a two-way table:

1. Identify the correct row/column total for the event described
2. Divide the relevant frequency by the appropriate total (the grand total, or a row/column total for conditional probabilities)

Two-way tables are a clear, systematic way to enumerate outcomes without missing any combinations.