Events One of Which equals Union/Examples/Target of Concentric Circles

Examples of Use of Events One of Which equals Union
Let $T$ be a target which consists of $10$ concentric circles $C_1$ to $C_{10}$ whose radii are respectively $r_k$ for $k = 1, 2, \ldots, 10$.

Let $r_k < r_{k + 1}$ for all $k = 1, 2, \ldots, 9$.

That is, let $C_1$ be the innermost and $C_{10}$ be the outermost.

Let $A_k$ denote the event of hitting $T$ inside the circle of radius $r_k$.

Let $B$ denote the event:
 * $B = \displaystyle \bigcup_{k \mathop = 1}^6 A_k$

Then $B$ is the event of hitting $T$ inside circle $C_6$.

Proof
By the geometry of the situation:
 * $C_1 \subseteq C_2 \subseteq \cdots \subseteq C_6$

By Events One of Which equals Union:

The result follows.