I don't understand what you've written for (c)
$\begin{align*}
&P[A \cap B] = \\ \\
&P[\text{1 tail}] = \\ \\
&\dbinom{3}{1} \left(\dfrac 1 2\right)^3 = \dfrac 3 8
\end{align*}$
If $A$ and $B$ are independent events then
$P[A \cap B] = P[A]P[B]$
from above
$P[A\cap B] = \dfrac 3 8 \neq \dfrac 1 4 = \left(\dfrac 1 2 \right )^2 = P[A]P[B]$
thus $A$ and $B$ are not independent.