The probability that a marksman will hit a target is given as `(1)/(5)`. Then, the probabiltiy that atleast one hit in 10 shots is

Options

A. `1-((4)/(5))^(10)`
B. `(1)/(5^(10))`
C. `1-(1)/(5^(10))`
D. None of these

Answer

A

Explanation

(a) Let X denotes 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)=""^(6)C_(r )((1)/(5))^(r )((4)/(5))^(10-r)`
`:.` Required probability `=P(X ge 1)=1-P(X=0)`
`=1-""^(10)C_(0)((1)/(5))^(0)((4)/(5))^(10)=1-((4)/(5))^(10)`