AQA A Level Maths: Statistics复习笔记3.1.2 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 (or lack of) between possible outcomes
• A Venn diagram consists of
  • a rectangle representing the sample space
  • a bubble (usually drawn as a circle/ellipse/oval) for each event
    • Bubbles may or may not overlap depending on which outcomes are shared between events
    • Bubble(s) is not a technical term but we like it!

How are Venn diagrams labelled and what do the numbers inside mean?

There is no standardised symbol used for this purpose

• Bubbles are labelled with their event name (A, B, etc)
• The numbers inside a Venn diagram (there should be one in each region) will represent either a frequency or a probability
  • In the case of probabilities being shown, all values should total 1

What do the different regions and bubbles overlapping mean on a Venn diagram?

• This will depend on how many events there are and how the outcomes overlap
• Venn diagrams show ‘AND’ and ‘OR’ statements easily
• Venn diagrams also instantly show mutually exclusive events
  • Independence can be deduced from the probabilities involved

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
  • i.e. fill in intersections (overlaps) first
  • This is particularly crucial with Venn diagrams with three events
    • Check a completed Venn diagram that the frequencies sum to the total involved or that probabilities sum to 1