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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer
    If \[P(A)=0.3,P(B)=0.6,P\left( \frac{B}{A} \right)=0.5\], then \[P(A\cup B)=\]

    A) 0.60                 

    B) 0.15           

    C) 0.75                             

    D) 0.65

    Correct Answer: C

    Solution :

    [c] \[P\left( A \right)=0.3\] \[P\left( \mathbf{B} \right)=0.6\] \[P\left( \frac{B}{A} \right)=0.5\] \[\Rightarrow \frac{P(A\cap B)}{P(A)}=0.5\] \[\Rightarrow P(A\cap B)=0.5\times 0.3=0.15\] \[\therefore ~P\left( A\cup B \right)=P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\] \[=0.3+0.6-0.15=0.9-0.15=0.75\] Hence, option [c] is correct.


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