1. Find the probability that one missile hits the target

For a missile to hit the target:

• it must not be intercepted, and then
• given that, it must hit the target.

Given: $P(\text{intercepted})=\frac{1}{3}$ So, $P(\text{not intercepted})=1-\frac{1}{3}=\frac{2}{3}$

Also, $P(\text{hit} \mid \text{not intercepted})=\frac{3}{4}$

Therefore, $P(\text{one missile hits})=P(\text{not intercepted})\cdot P(\text{hit} \mid \text{not intercepted})$ $=\frac{2}{3}\cdot \frac{3}{4}=\frac{1}{2}$

2. Find the probability that all three missiles hit

The three missiles are fired independently, so the events of their hitting are independent.

Thus, $P(\text{all three hit})=\left(\frac{1}{2}\right)^3=\frac{1}{8}$

3. Match with the options

$\frac{1}{8}$ corresponds to Option D.

Therefore, the correct answer is: $\boxed{\frac{1}{8}}$