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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    The probability that at least one of the events \[\mathbf{A}\And \mathbf{B}\] occurred is 0.7 and they occurs simultaneously with probability 0.2. Then \[\mathbf{p}(A)+\mathbf{P}\left( B \right)=\]

    A)  1.2                              

    B)  1.1           

    C)  0.1                              

    D)  1.5

    Correct Answer: B

    Solution :

    [b] Given that. \[P\left( A\cap B \right)=0.7\] \[P\left( A\cap B \right)=0.2\] \[\therefore \,\,P\left( \overline{A} \right)+P\left( \overline{B} \right)=1-P\left( A \right)+1-P\left( B \right)\]                         \[=2-\left[ P\left( A \right)+P\left( B \right) \right]\] \[\because P\left( A\cup B \right)=P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\] \[\Rightarrow \]\[P\left( A \right)+P\left( B \right)=P\left( A\cup B \right)+P\left( A\cap B \right)\] \[\Rightarrow \]\[P\left( A \right)+P\left( B \right)=0.7+0.2\] \[\Rightarrow \]\[P(A)+P(B)=0.9\] Now, \[P\left( A \right)+P\left( B \right)=2-\left[ P\left( A \right)+P\left( B \right) \right]\] \[=2-0.9=1.1\] Hence, option [b] is correct.


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