Question

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

Explanation:

Part (a)

Step1: Understand the complement of an event

The complement of event \( B\), denoted as \(\overline{B}\), consists of all outcomes in the sample space \( S\) that are not in \( B\).

Step2: Shade the appropriate region

In the Venn - diagram, shade the region of the sample space \( S\) that is outside the circle representing event \( B\).

Part (b)

Step1: Understand the intersection of two events

The intersection \(A\cap B\) consists of all outcomes that are in both event \(A\) and event \(B\).

Step2: Shade the appropriate region

In the Venn - diagram, shade the overlapping region (the region that is common to both the circle representing event \(A\) and the circle representing event \(B\)).

Answer:

For part (a), shade the region of \(S\) not in \(B\). For part (b), shade the overlapping region of \(A\) and \(B\).