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.\) shade \\(\overline{b}\cap\overline{d}\\) on the venn diagram.

Explanation:

Step1: Understand the meaning of $\overline{B}\cap\overline{D}$

$\overline{B}$ is the complement of event $B$ (all elements not in $B$), and $\overline{D}$ is the complement of event $D$ (all elements not in $D$). The intersection $\overline{B}\cap\overline{D}$ means the set of elements that are in both $\overline{B}$ and $\overline{D}$, i.e., elements that are neither in $B$ nor in $D$.

Step2: Identify the region on the Venn - diagram

The region that is outside both circle $B$ and circle $D$ within the sample - space $S$ is the region to be shaded.

Answer:

Shade the region of the sample - space $S$ that is outside both circle $B$ and circle $D$.