If the chance that a vessel arrives safely at a port is 910 then what is the chance that out of 5 vessels expected at least 4 will arrive safely?

Answer: Option A

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,
$$={}^5{C}_4\times {\left(\frac{9}{10}\right)}^4\left(\frac{1}{10}\right)+$$     $${\left(\frac{9}{10}\right)}^5$$
$$=\frac{14\times 9^4}{{10}^5}$$