Question

A rifleman is firing at a distant target and has only $10\%$ chance of hitting it. The minimum number of round he must fire in order to have $50\%$chance of hitting it at least once i

• A. $7$
• B. $8$
• C. $9$
• D. $6$

Answer 1

The correct option is A

$7$

Explanation for the correct option:

Step 1 : Find probability of hitting target in $1$ shot and that of not hitting the target

The probability of hitting the target in $1$ shot $=\frac{10}{100}$

$=\frac{1}{10}$

The probability of not hitting the target $=1-\left(\frac{1}{10}\right)$

$=\frac{9}{10}$

Step 2. : Find the probability of hitting once in $\text{'}n\text{'}$ shots

The probability of hitting once in $\text{'}n\text{'}$ shots $=1-{\left(\frac{9}{10}\right)}^n$

According to question,

$1-{\left(\frac{9}{10}\right)}^n=\frac{1}{2}$

$\Rightarrow$ ${\left(\frac{9}{10}\right)}^n=\frac{1}{2}$

Step 3. Taking log on both the sides

$n\log \frac{9}{10}=\log \frac{1}{2}$

$\Rightarrow$ $n=\frac{\log 0.5}{\log 0.9}$

$\Rightarrow$ $n=6.58~\mathbf{7}$

Hence, Option ‘A’ is Correct.