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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

  • question_answer
        For any two independent events \[{{\left( \frac{1}{4}+\frac{3}{4} \right)}^{9}}\] anc \[{{\left( \frac{3}{4}+\frac{1}{4} \right)}^{9}}\], \[\frac{1}{2}\]) is equal to :

    A)  \[r<-1\]

    B)  \[r=-1\]

    C)  \[r=0\]

    D)   none of these

    Correct Answer: A

    Solution :

                    Since \[{{\overline{E}}_{1}}\cap {{\overline{E}}_{2}}=\overline{{{E}_{1}}\cup {{E}_{2}}}\] and \[({{E}_{1}}\cup {{E}_{2}})\cap (\overline{{{E}_{1}}\cup {{E}_{2}}})=\phi \] \[P\{({{E}_{1}}\cup {{E}_{2}})\cap ({{\overline{E}}_{1}}\cap {{\overline{E}}_{2}})\}\]                                 \[=P(\phi )=0<\frac{1}{4}\]


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