The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$. The probability that the target will be hit if both A and B shoot at it independently is:

$\frac{11}{15}$

The correct answer is Option (1) → $\frac{11}{15}$

$\text{P(A hits)} = \frac{1}{5}, \quad \text{P(A misses)} = 1 - \frac{1}{5} = \frac{4}{5}$

$\text{P(B hits)} = \frac{2}{3}, \quad \text{P(B misses)} = 1 - \frac{2}{3} = \frac{1}{3}$

$\text{P(both A and B miss)} = \frac{4}{5} \cdot \frac{1}{3} = \frac{4}{15}$

$\text{P(at least one hits)} = 1 - \text{P(both miss)} = 1 - \frac{4}{15} = \frac{11}{15}$

Therefore, the probability that the target is hit is $\frac{11}{15}$.