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Previous Year Question (PYQs)
2
The probability of shooter hitting a target is $\dfrac{3}{4}$.
Find the minimum number of shots required so that the probability of hitting the target
at least once is more than $0.99$.
Solution
Probability of missing once = $\dfrac{1}{4}$.
Probability of missing all $n$ times = $(\dfrac{1}{4})^n$.
Hence, probability of hitting at least once = $1 - (\dfrac{1}{4})^n > 0.99$.
$\Rightarrow (\dfrac{1}{4})^n < 0.01$
$\Rightarrow n \log 4 > 2 \Rightarrow n > 1.66.$
Thus minimum $n = 3$.
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