Question

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

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

Answer 1

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

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 $P\left(E\right)=1-P\left(nohitinall10shots\right)\Rightarrow P\left(E\right)=1-{\left(\frac{4}{5}\right)}^{10}$