Answer
Not 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 neither die $1$ and $B$ denotes exactly one die is $2$.
We can see that $P(A)=\dfrac{n(A)}{n(S)}=\dfrac{25}{36}$ and
$P(B)=\dfrac{n(B)}{n(S)}=\dfrac{10}{36}=\dfrac{5}{18}$
Next, we find that there are nine outcomes that can be possible.
So, $P(A \cap B)=\dfrac{n(A \cap B)}{n(S)}=\dfrac{8}{36}=\dfrac{2}{9}$
Also, $P(A \cap B)=\dfrac{2}{9}$ and $P(A) P(B)=(\dfrac{25}{36})(\dfrac{5}{18})=\dfrac{125}{648}$
This means that condition (1) is satisfied. So, both $A$ and $B$ are Not independent events.
