Question

in the venn - diagram below, b and d are events in the sample space s. (note: for any event x, we use $overline{x}$ to denote
ot x.\) (a) shade $overline{d}$. (b) shade $bcup d$.

Explanation:

Step1: Recall the meaning of complement

The complement of an event \(D\), \(\overline{D}\), consists of all elements in the sample - space \(S\) that are not in \(D\). So, shade the entire region of \(S\) except the circle representing \(D\).

Step2: Recall the meaning of union

The union of two events \(B\) and \(D\), \(B\cup D\), consists of all elements that are in \(B\) or in \(D\) (or in both). So, shade the entire region of the circle \(B\), the entire region of the circle \(D\), and the overlapping region of \(B\) and \(D\).

Since this is a visual - based problem and we can't actually draw in this text - based format, the instructions for shading are the answer.

Answer:

(a) Shade the entire sample - space \(S\) except the circle representing \(D\).
(b) Shade the entire circle \(B\), the entire circle \(D\), and the overlapping region of \(B\) and \(D\).