Answer
Independent
Work Step by Step
We know that both $A$ and $B$ are independent events when it satisfies the following condition such that $P(A \cap B)=P(A) P(B) ~~~(1)$
Here, $A$ denotes the red die is $1$ and $B$ denotes the sum is even.
We can see that $P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{36}=\dfrac{1}{6}$ and
$P(B)=\dfrac{n(B)}{n(S)}=\dfrac{18}{36}=\dfrac{1}{2}$
Next, we find that there are nine outcomes that can be possible.
So, $P(A \cap B)=\dfrac{n(A \cap B)}{n(S)}=\dfrac{3}{36}=\dfrac{1}{12}$
Also, $P(A \cap B)=\dfrac{1}{12}$ and $P(A) P(B)=(\dfrac{1}{6})(\dfrac{1}{2})=\dfrac{1}{12}$
This means that condition (1) is satisfied. So, both $A$ and $B$ are independent events.