Probability - Describing mathematical events in words Consider a target that consists of $5$ concentric circles with radii  $1, 2, 3, 4, 5$ respectively. An event $A_j$, $j \in \{1,..,5\}$  describes a shot landing in the circle with the radius $j$. Describe the following events in words: 


*

*$\bigcap\limits_{k=1}^{3} A_{k}$

*$\bigcup\limits_{k=1}^{4} A_{k}$

*$ (A_3 \setminus A_2) ∪ (A_2 \setminus A_3)$

*$A_2^c ∩ A_3$
My attempt: 


*

*The shot lands in the circle with radius $1$ (Question: Since we're looking at the intersection of the sets, what role does $3$ play here? Wouldn't we be describing the same event if we let $k$ go to $4$ and $5$?)  

*The shot lands in circle $1, 2, 3$ or $ 4. $

*The shot lands in circle $2$ or $3$. 

*The shot lands in circle $3$. 
Are my answers correct? Any help would be much appreciated. 

Your answer to 1 is correct.  If you added in the other two circles it wouldn't change anything because $A_1$ is a subset of all the others.  Any intersection that includes $A_1$ will just be $A_1$ in this case.  
Your answer to $2$ is correct but may be marked down.  As in 1, you are expected to realize that $A_4$ is a superset of the other three, so the union is just $A_4$.  
For 3 it must land in circle $3$ but not in circle $2$.  That is the point of the setminus.  
For 4 it is the same answer as $3$.
