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# If on an average 2 ships in every 10, sinks. The probability that out of 5 ships expected to arrive, at least three will arrive safely is

$\begin {array} {1 1} (A)\;\large\frac{2944}{3125} & \quad (B)\;\large\frac{2946}{3125} \\ (C)\;\large\frac{2948}{3125} & \quad (D)\;None\: of \: these \end {array}$

Here $n = 5$
P = probability of safe arrival of one ship
$= \large\frac{4}{5}$
$q = \large\frac{1}{5}$
$P(3)+P(4)+P(5)=5C_3 (415)^3 \bigg( \large\frac{1}{5} \bigg)^2+5C_4 (415)^4 \bigg( \large\frac{1}{5} \bigg)+$
$5C_5 (415)^5 \bigg( \large\frac{1}{5} \bigg)^0$
$= \large\frac{640+1280+1024}{55}$
$= \large\frac{2944}{3125}$
Ans : (A)

–1 vote