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What is probability?

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).

Probability explained

For equally likely outcomes, probability is favourable outcomes divided by total outcomes. Tree diagrams and Venn diagrams organise multi-stage and overlapping events.
Two rules carry most marks: multiply along the branches for 'and', add distinct outcomes for 'or', and subtract from 1 for 'at least one'.

Key formula

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)

Worked example

Drawing two red counters without replacement from 3 red and 5 blue: 38×27=328\frac{3}{8} \times \frac{2}{7} = \frac{3}{28}.

Examiner tip

Watch for 'without replacement' — the second denominator must drop by one. It is the single most common error in probability questions.

Probability: common questions

What does mutually exclusive mean?
Two events that cannot both happen, so the probability of their intersection is zero and you simply add their probabilities.
What is conditional probability?
The probability of one event given another has already happened, written P(A | B) and calculated as P(A ∩ B) ÷ P(B).

Related terms

Normal distribution

The normal distribution is a symmetric, bell-shaped continuous probability distribution defined by its mean and standard deviation.

Mean, median and mode

The mean, median and mode are three averages: the arithmetic average, the middle value in order, and the most frequent value.

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