Question

A rifle man firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it atleast once is

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

The correct option is B 7

The probability of hitting in one shot =$\frac{10}{100}=\frac{1}{10}$
If he fires n shots, the probability of hitting atleast one
$=1-{(1-\frac{1}{10})}^n=1-{\left(\frac{9}{10}\right)}^n=50\%=\frac{50}{100}=\frac{1}{2}\Rightarrow {\left(\frac{9}{10}\right)}^n=\left(\frac{1}{2}\right)$
$\therefore n\{log9-log10\}=log1-log2\Rightarrow n\{2log3-1\}=0-log2\therefore n=\frac{log2}{1-2log3}=\frac{0.3010300}{1-2\times 0.4771213}=6.6$
Hence, n =7