Events One of Which equals Intersection/Examples

Examples of Use of Events One of Which equals Intersection

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 $C$ denote the event:

$C = \ds \bigcap_{k \mathop = 5}^{10} A_k$

Then $C$ is the event of hitting $T$ inside circle $C_5$.