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  • A man firing at a distant target has 10% chance of hitting the target in one shot. The number of times he must fire at the target to have about 50 % chance of hilting the target is

A man firing at a distant target has 10% chance of hitting the target in one shot. The number of times he must fire at the target to have about 50 % chance of hilting the target is

 

Option: 1

11


Option: 2

9


Option: 3

7


Option: 4

5


Answers (1)

best_answer

The probability of hitting in one shot \mathrm{=\frac{10}{100}=\frac{1}{10}}
If he fires n shots, the probability of hitting at least once

\begin{array}{ll} & = \mathrm{1-\left(1-\frac{1}{10}\right)^n=1-\left(\frac{9}{10}\right)^n=\frac{1}{2}} \text { (from the question) } \\ \\\therefore & \mathrm{\left(\frac{9}{10}\right)^n}=\frac{1}{2} \\ \\\therefore \quad & \mathrm{n\left\{2 \log _{10} 3-1\right\}=-\log _{10} 2} \\ \\\therefore & \mathrm{n=\frac{\log _{10} 2}{1-2 \log _{10} 3}=\frac{0.3010}{1-2 \times 0.4771}=6.5} \text { (nearly) } \end{array}

\therefore  for 6 shots, the probability is about 53 % while for 7 shots it is nearly 48 %

Posted by

Sanket Gandhi

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