The probability that a marksman will hit a target is given as 1/5. Then the probability that at least one hit in 10 shots is

$1-\left(\frac{4}{5}\right)^{10}$

Let X denote the number of shots in which a marksman hit a target in 10 shots. Then, the probability of r hits is given by

$P(X=r)={^{10}C}_r\left(\frac{1}{5}\right)^{r}\left(\frac{4}{5}\right)^{10-r}$

∴ Required probability $=P(X ≥ 1)= 1 - P(X=0)$

$= 1- {^{10}C}_0\left(\frac{1}{5}\right)^{0}\left(\frac{4}{5}\right)^{10}=1- \left(\frac{4}{5}\right)^{10}$