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# If the chance that a ship will arrive safely at a port is $\large\frac{9}{10}$, the chance that out of 5 ships expected to arrive at the port at least 4 will arrive safely is

$\begin {array} {1 1} (A)\;\large\frac{91854}{100000} & \quad (B)\;\large\frac{91827}{100000} \\ (C)\;\large\frac{91881}{100000} & \quad (D)\;None\: of \: these \end {array}$

Here = 5
P = P( safe arrival of one ship ) = $\large\frac{9}{10}$
$Q = \large\frac{1}{10}$
Hence $P(4)+P(5) = 5C_4 \bigg( \large\frac{9}{10} \bigg)^4 \bigg( \large\frac{1}{10} \bigg)^1 + 5C_5 \bigg( \large\frac{9}{10} \bigg)^5 \bigg( \large\frac{1}{10} \bigg)^0$
$= \large\frac{32805+59049}{105}$
$= \large\frac{91854}{100000}$
Ans : (A)

–1 vote