A Venn diagram is a visual tool used to illustrate relationships between sets or events. Each event is represented by a circle, and overlaps between circles represent shared outcomes. This helps you clearly see intersections (outcomes common to events), unions (all outcomes in any event), and mutually exclusive events (no overlap).

Example

Using the following Venn diagram, find

\mathop{n}\left(U\right)
\mathop{P}\left(A\cap B\right)
\mathop{P}\left(A\cap C\right)
\mathop{P}\left(A^{\prime}\cup C\right)

In the above Venn diagram, we start by noticing

\mathop{n}\left(U\right)=5+2+11+3+8=\boxed{29}

We also notice that A and B do not overlap - so they are mutually independent:

\mathop{P}\left(A\cap B\right)=\boxed{0}

We see that the region shared by A and C has a 2, so

\mathop{P}\left(A\cap C\right)=\boxed{\frac{2}{29}}

Finally

\mathop{P}\left(A^{\prime}\cap C\right)=\mathop{P}\left(C\right)-\mathop{P}\left(C\cap A\right)=\frac{15-2}{29}=\boxed{\frac{13}{29}}

Probability