Question

in the venn diagram below, a 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 \\(a\cap d\\).

Explanation:

Step1: Recall the meaning of $\overline{D}$

$\overline{D}$ represents all elements not in $D$. So we shade the area of the sample - space $S$ that is outside of circle $D$.

Step2: Recall the meaning of $A\cap D$

$A\cap D$ represents the intersection of $A$ and $D$, i.e., the elements that are in both $A$ and $D$. So we shade the overlapping region of circle $A$ and circle $D$.

Answer:

(a) Shade the area of the rectangle $S$ that is outside of circle $D$.
(b) Shade the overlapping region of circle $A$ and circle $D$.