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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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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

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


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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)
answered Jan 4, 2014 by thanvigandhi_1

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