Question

If a certain missile will hit the target once out of four times and four such missiles are fired at the same target, then what is the probability that the target be hit atleast once?

• A. $1$
• B. $\frac{51}{256}$
• C. $\frac{175}{256}$
• D. None of these

Answer 1

The correct option is C

$\frac{175}{256}$

It is given that the missile will hit the target once out of four times.
$\Rightarrow$ Probability that the target being hit = $\frac{1}{4}$
$\Rightarrow$ Probability that the target won't be hit = $1-\frac{1}{4}$ = $\frac{3}{4}$
Here, four missiles are fired.
$\Rightarrow$ Probability that the target is being hit atleast once
= 1 - Probability that all the four targets won't be hit
= 1 - $(\frac{3}{4}\times \frac{3}{4}\times \frac{3}{4}\times \frac{3}{4})$
= 1 - ${\left(\frac{3}{4}\right)}^4$
= 1 - $\left(\frac{81}{256}\right)$
= $\frac{175}{256}$
$\therefore$ The required probability is $\frac{175}{256}$.