Venn Diagrams with Conditional Probability (Cambridge (CIE) AS Maths: Probability & Statistics 1): Revision Note

Further Venn Diagrams

What do you mean by further Venn diagrams?

• The Venn diagrams used here are no more complicated than those in the first Venn Diagrams revision note, however

  • questions may use set notation as well, or alongside contextual questions

  • there may be more detailed use of conditional probability

  • mutually exclusive, three events and other unusual Venn diagram setups may be involved

How do I solve conditional probability problems using Venn diagrams?

• Interpreting questions in terms of AND ($\cup$), OR ($\cap$), complement ( ‘ ) and
  “given that” ( | )

• Use mini-Venn diagrams to sketch and shade the regions you are dealing with – use different colours if available or different styles of shading if not

  • Shading can help you see the answer

since $\mathrm{P}\left(A\right|B)=\frac{\mathrm{P}(A\mathit{\cap }B)}{\mathrm{P}\left(B\right)}$ shade B  first, then shade $A\cap B$

the answer will then be $\frac{"\mathrm{double}\mathrm{shading}"}{"\mathrm{single}\mathrm{shading}"}$