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