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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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Let A and B be two independent events such that $P(A) = \large\frac{1}{5} \: P( A \cup B ) = \large\frac{7}{10}$. Ten $ P(\overline B)$ is equal to

$\begin {array} {1 1} (A)\;\large\frac{3}{8} & \quad (B)\;\large\frac{2}{7} \\ (C)\;\large\frac{7}{9} & \quad (D)\;None\: of \: these \end {array}$

 

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1 Answer

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Let $ P( \overline B ) = x$ Then $P(B)=1-x$
$P(A \cap B)=P(A) . P(B)$
$ = \large\frac{1}{5} (1-x)$
$P(A \cup B )=P(A)+P(B)-P(A \cap B )$
$ \large\frac{7}{10} = \large\frac{1}{5} +(1-x) - \large\frac{1}{5} (1-x)$
$ \large\frac{1}{2}=\large\frac{4}{5} (1-x)$
$ 1-x = \large\frac{5}{8}$
$ x = \large\frac{3}{8}$
Ans : (A)
answered Jan 8, 2014 by thanvigandhi_1
 

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