If the chance that a vessel arrives safely at a port is $$\frac{{9}}{{10}}$$ then what is the chance that out of 5 vessels expected at least 4 will arrive safely?

A. $$\frac{{14 \times {9^4}}}{{{{10}^5}}}$$

B. $$\frac{{15 \times {9^5}}}{{{{10}^4}}}$$

C. $$\frac{{14 \times {9^3}}}{{{{10}^4}}}$$

D. $$\frac{{14 \times {9^6}}}{{{{10}^5}}}$$

Answer: Option A

Solution(By Examveda Team)

The probability that exactly 4 vessels arrive safely is,
$${ = ^5}{C_4} \times {\left( {\frac{9}{{10}}} \right)^4}\left( {\frac{1}{{10}}} \right)$$
The probability that all 5 arrive safely is $${\left( {\frac{9}{{10}}} \right)^5}$$
The probability that at-least 4 vessels arrive safely,
$$ = {}^5{C_4} \times {\left( {\frac{9}{{10}}} \right)^4}\left( {\frac{1}{{10}}} \right) + $$     $${\left( {\frac{9}{{10}}} \right)^5}$$
$$ = \frac{{14 \times {9^4}}}{{{{10}^5}}}$$