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

Source Work

 * $\text I$ Random Events
 * $1$. Relations among Random Events
 * Problem $3$
 * Problem $3$

Mistake

 * A target consists of $10$ concentric circles of radius $r_k (k = 1, 2, 3, \ldots, 10)$. An event $A_k$ means hitting the interior of a circle of radius $r_k (k = 1, 2, \ldots, 10)$. What do the following events mean?
 * $\displaystyle B = \bigcup_{k \mathop = 1}^6 A_k, \qquad C = \prod_{k \mathop = 5}^{10} A_k$?

Note that in the above, $C = \prod_{k \mathop = 5}^{10} A_k$ is the notation that uses for what we on  would write $C = \bigcap_{k \mathop = 5}^{10} A_k$.

Correction
The question fails to state whether the circle radius $r_1$ or the circle radius $r_{10}$ is the innermost.

It is not obvious: it is feasible for the circles to have been numbered according to the score that the archer would achieve, in which case $r_{10}$ would be innermost.

However, that arrangement would be inconsistent with the answer given in the back of the book, and so it is apparent that:
 * $r_k < r_{k + 1}$

for $k = 1, 2, \ldots, 9$.