Question

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

Explanation:

Part (a)

Step1: Understanding the complement of an event

The complement of an event \(C\), denoted as \(\overline{C}\), consists of all the outcomes in the sample space \(S\) that are not in \(C\). So, we need to shade the region of the Venn - diagram that is inside \(S\) but outside \(C\).

Part (b)

Step1: Understanding the union of two events

The union of two events \(A\) and \(C\), denoted as \(A\cup C\), consists of all the outcomes that are in \(A\) or in \(C\) or in both. So, we need to shade the region of the Venn - diagram that is inside \(A\) or inside \(C\) (including the overlapping region).

Answer:

• (a) Shade the region of the Venn - diagram that is inside the rectangle \(S\) but outside the circle \(C\).
• (b) Shade the region of the Venn - diagram that is inside the circle \(A\) or inside the circle \(C\) (including the intersection of \(A\) and \(C\)).