Question

The probability of a man hitting a target is $\frac{1}{10}$. The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$, is

Answer 1

We have,
$1-\text{(probability of all shots result in failure)}>\frac{1}{4}$
$\Rightarrow 1-{\left(\frac{9}{10}\right)}^n>\frac{1}{4}$
$\Rightarrow {\left(\frac{9}{10}\right)}^n<\frac{3}{4}$
$\Rightarrow n\ge 3$