Shading the complement of a union on a Venn diagram, the size and probability of an intersection, and why two events are not mutually exclusive

In the Venn diagram below, the rectangle represents a sample space \(U\) of equally likely outcomes, and the two ovals represent the events \(A\) and \(B\). The numbers of outcomes are \(n(U)=36\), \(n(A)=11\), \(n(B)=6\) and \(n\left((A\cup B)'\right)=21\).

1. Shade the region \((A\cup B)'\) on the Venn diagram.
2. Find
   1. \(n(A\cap B)\);
   2. \(\mathrm{P}(A\cap B)\).
3. Explain why the events \(A\) and \(B\) are not mutually exclusive.

[4]