Example 2. Experiment - tossing a die. Events: $A_{k}(k=1,2,3,4,5,6)$ - "$k$ points fall", $A$ - "an even number of points falls", $B$ - "an odd number of points falls", $C$ - "a number of points that is a multiple of three falls", $D$ - "a number of points greater than three falls". Express events $A, B, C$ and $D$ in terms of events $A_{k}$.
The solution is as follows. Event $A$ occurs if and only if $A_{2}$, or $A_{4}$, or $A_{6}$ occurs. This means that $A=A_{2}+A_{4}+A_{6}$. Reasoning in a similar manner, we get: $\quad B=A_{1}+A_{3}+A_{5}, \quad C=A_{3}+A_{6}$, $D=A_{4}+A_{5}+A_{6}$.