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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-2

  • question_answer
    A, B, C be three exhaustive and mutually exclusive events associated with a random experiment. If \[\mathbf{P}\left( B \right)=-\mathbf{P}\left( A \right)\]and\[\mathbf{P}\left( C \right)=-\mathbf{P}\left( B \right)\],the \[\mathbf{P}\left( A \right)\]is equal to:

    A) \[\frac{8}{13}\]                         

    B) \[\frac{7}{13}\]            

    C) \[\frac{6}{13}\]                         

    D) \[\frac{4}{13}\]

    Correct Answer: D

    Solution :

    [d] \[\because A,B\And C\]be exhaustive & mutually exclusive events. \[\therefore P\left( A\cup B\cup C \right)=P\left( A \right)+P\left( B \right)+P\left( C \right)\] \[1=x+\frac{3}{2}x+\frac{1}{2}\times \frac{3}{2}x\]   (Say \[P\left( A \right)=x)\] \[1=x+\frac{3x}{2}+\frac{3x}{4}=\frac{4x+6x+3x}{4}\] \[\Rightarrow \frac{13x}{4}=1\Rightarrow x=\frac{4}{13}\]. i.e. \[P\left( A \right)x=\frac{4}{13}\]So, option [d] is correct.


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