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 b \cup d.

Explanation:

Step1: Understand the complement of an event

The complement of event \(D\), denoted as \(\overline{D}\), consists of all outcomes in the sample space \(S\) that are not in \(D\). So, we shade the region of \(S\) that is outside the circle \(D\).

Step2: Understand the union of two events

The union of events \(B\) and \(D\), denoted as \(B\cup D\), consists of all outcomes that are in \(B\) or in \(D\) or in both. So, we shade the region of \(B\) (the entire circle \(B\)) and the region of \(D\) (the entire circle \(D\)).

Answer:

For part (a), shade the region of the sample space \(S\) that is outside the circle \(D\). For part (b), shade the entire circle \(B\) and the entire circle \(D\).