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Previous Year Question (PYQs)



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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