Question

The probability that a marksman will hit a target is given as $\frac{1}{5}.$ Then the probability that he hits at least once in $10$ shots is

• A. $1-{\left(\frac{4}{5}\right)}^{10}$
• B. $\frac{1}{5^{10}}$
• C. $1-\left(\frac{1}{5^{10}}\right)$
• D. ${\left(\frac{4}{5}\right)}^{10}$

Answer 1

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

Let $H$ be the event of hitting the shot, then
$P\left(\overline{H}\right)=1-P\left(H\right)=1-\frac{1}{5}=\frac{4}{5}$
Now let $E$ be the event of hitting at least once in $10$ shots
Then $P\left(E\right)=1-P$ (no hit in all $10$ shots)
$\Rightarrow P\left(E\right)=1-{\left(\frac{4}{5}\right)}^{10}$