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 $10$ shoots is

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

Answer 1

The correct option is A

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

The explanation for the correct answer.

Solve for the probability of at least one hit in $10$ shoots

The probability that a marksman hit a target, $P\left(A\right)=\frac{1}{5}$

The probability that a marksman will not hit the target, $P(A\text{'})=\frac{4}{5}$

The probability that he will not hit the target in ten shots $={\left(\frac{4}{5}\right)}^{10}$

Hence, the probability that at least one hit in $10$shots $=1-{\left(\frac{4}{5}\right)}^{10}$

Hence, option(A) is the correct answer.