Venn Diagrams (DP IB Analysis & Approaches (AA)): Revision Note

Venn diagrams

What is a Venn diagram?

• A Venn diagram is a way to illustrate events from an experiment and are particularly useful when there is an overlap between possible outcomes

• A Venn diagram consists of

  • a rectangle representing the sample space (U)

    • The rectangle is labelled U 

    • Some mathematicians instead use S or ξ 

  • a circle for each event

    • Circles may or may not overlap depending on which outcomes are shared between events

• The numbers in the circles represent either the frequency of that event or the probability of that event

  • If the frequencies are used then they should add up to the total frequency

  • If the probabilities are used then they should add up to 1

What do the different regions mean on a Venn diagram? 

• is represented by the regions that are not in the A circle

• is represented by the region where the A and B circles overlap

• is represented by the regions that are in A or B or both

• Venn diagrams show ‘AND’ and ‘OR’ statements easily

• Venn diagrams also instantly show mutually exclusive events as these circles will not overlap

• Independent events cannot be seen instantly

  • You need to use probabilities to deduce if two events are independent

How do I solve probability problems involving Venn diagrams?

• Draw, or add to a given Venn diagram, filling in as many values as possible from the information provided in the question

• It is usually helpful to work from the centre outwards

  • Fill in intersections (overlaps) first

• If two events are independent you can use the formula

  • 

• To find the conditional probability 

  • Add together the frequencies/probabilities in the B circle

    • This is your denominator

  • Out of those frequencies/probabilities add together the ones that are also in the A circle

    • This is your numerator

  • Evaluate the fraction