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 a ∩ b. (b) shade $overline{a}$.

Explanation:

Step1: Recall intersection definition

$A\cap B$ is the set of elements that are in both $A$ and $B$. So, shade the overlapping part of circles $A$ and $B$.

Step2: Recall complement definition

$\overline{A}$ is the set of elements that are not in $A$. So, shade the part of the sample - space $S$ that is outside of circle $A$.

Answer:

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