Answer: $\mathrm {\bf C}$
Explanation:
We know that the first throw showed $4$.
Thus the second and third die throws must sum to $11$ in order to get the total sum as $15$
With six-sided dice, there are only two possible combinations for two throws to sum = $11$
$(5,6)$ or $(6, 5)$
There are $36$ possible combinations and $2$ are favorable.
Hence, probability = $\frac{2}{36}=\frac{1}{18}$
$\therefore \mathbf C$ is the correct option.