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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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If A and B are two events such that $ P ( A \cup B) = \large\frac{5}{6}, \: P ( A \cap B ) = \large\frac{1}{3} \: and \: P(B') = \large\frac{1}{2}$ then events A and B are

$\begin {array} {1 1} (1)\;dependent & \quad (2)\;independent \\ (3)\;mutually\: exclusive & \quad (4)\;none\: of \: these \end {array}$

 

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1 Answer

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$ P (B') = \large\frac{1}{2}$
$ \Rightarrow P (B) = \large\frac{1}{2}$
$ P ( A \cup B ) = \large\frac{5}{6}$
$ \Rightarrow P ( A) + P (B) - P ( A \cap B ) = \large\frac{5}{6}$
$ \Rightarrow P (A) + \large\frac{1}{2}-\large\frac{1}{3}=\large\frac{5}{6}$
$ P(A) = \large\frac{2}{3}$
Now $ P(A)\: P(B)= \bigg( \large\frac{ \not{2} }{3} \bigg) \bigg( \large\frac{1}{ \not{2} } \bigg)$
$ = \large\frac{1}{3}$
$ P ( A \cap B ) = \large\frac{1}{3}$
$ \therefore $ A and B are independent
answered Jan 2, 2014 by thanvigandhi_1
 

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