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 ∪ b.

Explanation:

Step1: Understand the complement

The complement of an event $B$, denoted as $\overline{B}$, consists of all elements in the sample - space $S$ that are not in $B$. So, we shade the entire region of $S$ except the circle representing $B$.

Step2: Understand the union

The union of two events $A$ and $B$, denoted as $A\cup B$, consists of all elements that are in $A$ or in $B$ or in both. So, we shade the entire region of circle $A$, circle $B$ and their intersection.

Answer:

(a) Shade the region of the sample - space $S$ that is outside the circle $B$.
(b) Shade the entire region of circle $A$, circle $B$ and the intersection of $A$ and $B$.