Everything Maths Grade 10

14.3 Venn diagrams EMA7Y

A Venn diagram is a graphical way of representing the relationships between sets. In each Venn diagram a set
is represented by a closed curve. The region inside the curve represents the elements that belong to the set,
while the region outside the curve represents the elements that are excluded from the set.

Venn diagrams are helpful for thinking about probability since we deal with different sets. Consider two events,
AandB, in a sample spaceS. The diagram below shows the possible ways in which the event sets can overlap,
represented using Venn diagrams:
S
A B

S

A

B

S

A

B

The sets are represented using a rectangle forSand circles for each ofAandB. In the first diagram the two
events overlap partially. In the second diagram the two events do not overlap at all. In the third diagram one
event is fully contained in the other. Note that events will always appear inside the sample space since the
sample space contains all possible outcomes of the experiment.

VISIT:

This video shows how to draw a Venn diagram using a deck of cards as the sample space.

See video:2GWCatwww.everythingmaths.co.za

Worked example 4: Venn diagrams

QUESTION

Represent the sample space of two rolled dice and the following two events using a Venn diagram:

• Event A: the sum of the dice equals 8


• Event B: at least one of the dice shows a 2
  SOLUTION

S

B

A

478 14.3. Venn diagrams