A Venn diagram can show how many members of a group are in each region. When one member is chosen at random, the probability of an event is the number of members in the regions for that event divided by the total number in the group. Add every region that the event covers and count the overlap once. The total includes the members outside the circles. Example The Venn diagram shows how many of 30 students play football (F) and tennis (T). **Event** | **Regions** | **Probability** plays both | 6 | (6)/(30)=(1)/(5) plays football | 9+6 | (15)/(30)=(1)/(2) plays at least one | 9+6+8 | (23)/(30) plays neither | 7 | (7)/(30) In Extended work these events may be written P(F T)=(1)/(5) and P(F T)=(23)/(30), and a diagram may have three sets. Core questions use two sets and words such as “both” and “at least one”.

A Venn diagram can show how many members of a group are in each region. When one member is chosen at random, the probability of an event is the number of members in the regions for that event divided by the total number in the group.

Add every region that the event covers and count the overlap once. The total includes the members outside the circles.

The Venn diagram shows how many of 30 students play football (\(F\)) and tennis (\(T\)).

In Extended work these events may be written \(\mathrm{P}(F\cap T)=\frac{1}{5}\) and \(\mathrm{P}(F\cup T)=\frac{23}{30}\), and a diagram may have three sets. Core questions use two sets and words such as “both” and “at least one”.

Probability

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Event	Regions	Probability
plays both	\(6\)	\(\frac{6}{30}=\frac{1}{5}\)
plays football	\(9+6\)	\(\frac{15}{30}=\frac{1}{2}\)
plays at least one	\(9+6+8\)	\(\frac{23}{30}\)
plays neither	\(7\)	\(\frac{7}{30}\)

Probabilities from a Venn diagram

Probabilities from a Venn diagram