When a missile is fired from a ship, the probability that it is intercepted is $$\frac{1}{3}$$ and the probability that the missile hits the target, given that it is not intercepted, is $$\frac{3}{4}$$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

The probability that a missile is intercepted is $$\frac{1}{3}$$, so the probability that it is not intercepted is $$1 - \frac{1}{3} = \frac{2}{3}$$.

Given that a missile is not intercepted, the probability that it hits the target is $$\frac{3}{4}$$.

Therefore, the probability that a single missile hits the target is $$P(\text{hit}) = P(\text{not intercepted}) \times P(\text{hit} \mid \text{not intercepted}) = \frac{2}{3} \times \frac{3}{4} = \frac{1}{2}$$.

Since three missiles are fired independently, the probability that all three hit the target is $$\left(\frac{1}{2}\right)^3 = \frac{1}{8}$$.