The probability that a marksman will hit a target is given is 1/5. Then the probability that at least once hit in 10 shots is `1-(4//5)^(10)` b. `1//5^(10)` c. `1-(1//5)^(10)` d. `(4//5)^(10)`

Options

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

Answer

A

Explanation

Let X denote the number of shots in which a markshman hit a target in 10 shots. Then, the probability of r hits is given by
`-P(X=r)=.^10C_r((1)/(5))^r((4)/(5))^10-r`
`therefore` Required Probability `P(X=ge1)=1-P(X=0)`
`=1-.^10C_0((1)/(5))^0((4)/(5))^10=1-((4)/(10))^10`.