Question

If $10$% of the attacking a air crafts are expected to be shot down before reaching the target, the probability that out of $5$ aircrafts atleast four will be shot before they reach the target is

• A. $4{\left(\frac{1}{10}\right)}^4$
• B. $5{\left(\frac{1}{10}\right)}^4$
• C. $\left(4.6\right){\left(\frac{1}{10}\right)}^4$
• D. $6{\left(\frac{1}{10}\right)}^4$

Answer 1

Answer: (C)

$\left(4.6\right){\left(\frac{1}{10}\right)}^4$

$P$ (shot before target) $=\frac{10}{100}=0.1$

$P$ (At least $4$ out of $5$ get shot)= $P\left(4shot\right)+P\left(5shot\right)$

$={}^5{C}_4{\left(\frac{1}{10}\right)}^4\left(\frac{9}{10}\right)+{}^5{C}_5{\left(\frac{1}{10}\right)}^5$

$=\frac{45}{{10}^5}+\frac{1}{{10}^5}$

$P$ (At least $4$ out of $5$ get shot)$=4.6\left(\frac{1}{{10}^4}\right)$

$C$ is correct