Cambridge IGCSE 0580 · Topic 9 of 10

Probability

Calculating probabilities, relative and expected frequency, combined events, tree and Venn diagrams, and conditional probability.

📌 Key points

Probability runs from 0 (impossible) to 1 (certain). For equally likely outcomes, P(event) = number of favourable outcomestotal number of outcomes.
P(not A) = 1 − P(A). The probabilities of all possible outcomes add up to 1.
Relative frequency = frequencynumber of trials; it is a better estimate of probability when there are more trials.
Expected frequency = probability × number of trials.
For mutually exclusive events (cannot happen together): P(A or B) = P(A) + P(B).
For independent events (one does not affect the other): P(A and B) = P(A) × P(B).
Tree diagrams: multiply along the branches, then add the results for the outcomes you want. Without replacement, the probabilities on the second branches change.
Sample space diagrams list all outcomes of two events; Venn diagrams and two-way tables organise data into groups.
Conditional probability: P(A given B) = P(A and B)P(B) — only count the outcomes inside B.

Outcome: A possible result of an experiment.
Event: One or more outcomes of an experiment.
Sample space: The list (or diagram) of all possible outcomes.
Relative frequency: How often an event happened ÷ the number of trials.
Expected frequency: Probability × number of trials.
Mutually exclusive: Events that cannot happen at the same time.
Independent events: Events where the outcome of one does not affect the other.
Conditional probability: The probability of an event given that another event has happened.

A bag has 5 red and 3 blue counters. Two are taken out without replacement. Find the probability that they are the same colour.

💡 Exam tip

Give probabilities as fractions, decimals or percentages — never as a ratio such as 3 : 8 or in words such as “3 out of 8”.

Test yourself8 questions from a bank of 22. A new mix every time.