A) 7
B) 8
C) 6
D) 5
Correct Answer: B
Solution :
[b] Let n denote the required number of shots and X the number of shots that hit the target. Then \[X\tilde{\ }B(n,p)\] with \[P=1/4.\] now, \[P(X\ge 1)\ge 0.9\Rightarrow 1-P(X=0)\ge 0.9\] \[\Rightarrow 1{{-}^{n}}{{C}_{0}}{{\left( \frac{3}{4} \right)}^{n}}\ge 0.9\Rightarrow {{\left( \frac{3}{4} \right)}^{n}}\le \frac{1}{10}\] \[\Rightarrow {{\left( \frac{4}{3} \right)}^{n}}\ge 10\Rightarrow n(log4-log3)\ge 1\] \[\Rightarrow n(0.602-0.477)\ge 1\Rightarrow n\ge \frac{1}{0.125}=8\] Therefore the least number of trials required is 8.
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