11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    \[\mathbf{P}\left( A \right)=\mathbf{0}.\mathbf{25}\]and \[\mathbf{P}\left( B \right)=\mathbf{0}.\mathbf{50}\]and \[\mathbf{P}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{0}.\mathbf{14}\]then \[\mathbf{P}\left( \mathbf{A}'\cap \mathbf{B}' \right)=?\]

    A)  \[\frac{11}{100}\]                    

    B)  \[\frac{39}{100}\]

    C)  \[\frac{35}{100}\]                    

    D)  \[\frac{22}{100}\]

    Correct Answer: B

    Solution :

    [b] \[\therefore P\left( A\cup B \right)=P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\] \[=0.25+0.50-0.14=0.75-0.14=0.361\] \[\therefore P({A}'\cap B')=p(\cup uB)'\] [By Demorgen's Law] \[=1-P\left( A\cup B \right)=1-0.61=0.39=\frac{39}{100}\]

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