Question

The probability that a marksman will hit a target is given as $\frac{1}{5}$ ,then his probability of at least one hit in 10 shots is

• A. $1-{\left(\frac{4}{5}\right)}^{10}$
• B. $\frac{1}{5^{10}}$
• C. $1-\frac{1}{5^{10}}$
• D. None of these

Answer 1

The correct option is A $1-{\left(\frac{4}{5}\right)}^{10}$

He will hit the target, $P\left(A\right)=\frac{1}{5}.$ He will not hit the target,$P\overline{\left(A\right)}=\frac{4}{5}.$ Probability that he
will not hit the target in 10 shoots is ${\left(\frac{4}{5}\right)}^{10}$
So, at least once, target will be hit.Required probability $=1-{\left(\frac{4}{5}\right)}^{10}$