Question

A rifleman is firing at a distant target and has only \(10 \%\) chance of hitting it. The least number of rounds he must fire to have more than \(50 \%\) chance of hitting it at least once, is
(A) 5
(B) 7
(C) 9
(D) 11

Answer 1

Ans:(B)
Hint: \(P\) (hitting a target) \(=\frac{1}{10}\)
\(\therefore \mathrm{P}(\) not hitting a target \()=\frac{9}{10}\)
\(\therefore\) Let number of trials \(=\mathrm{n}\)
So, \(P\) (hitting at least once) \(=1-P\) (missing all) \(=1-\left(\frac{9}{10}\right)^{n} \geq \frac{1}{2}\) \(\Rightarrow(0.9)^{\mathrm{n}} \leq 0.5\)
\((0.9)^{6}=0.531441,(0.9)^{7}=0.4782969 \Rightarrow \mathrm{n}=7\)