Venn Diagrams with Conditional Probability (OCR A Level Maths A: Statistics): Revision Note

Three events, $A,B$ and $C$ are such that

        events $A$ and $C$ are mutually exclusive

        $$\begin{gathered} \mathrm{P}(A\cap B)=0.2 \\ \mathrm{P}(B\cap C)=0.3 \\ \mathrm{P}\left(\right(A\cup B\cup C)\text{'})=0.1 \\ \mathrm{P}\left(B\right)=0.7 \\ \mathrm{P}(A\text{'})=0.75. \end{gathered}$$

(a) Draw a complete Venn diagram to show the probabilities connecting the three events.

 (b) Find 

(i) $\mathrm{P}\left(A\right|B)$

(ii) $\mathrm{P}(A\text{'}|C\text{'})$

(iii) $\mathrm{P}\left(C\right|(A\cup B)\text{'})$

Answer:

• Always draw the box in a Venn diagram; it represents all possible outcomes of the experiment so is a crucial part of the diagram, the bubbles merely represent the events we are particularly interested in

• You may be able to answer some questions by applying formulae or you may prefer to use shaded mini-Venn diagrams; complicated questions tend to be easier with mini-Venn diagrams