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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-6

  • question_answer
    Two events A and B have probability 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is

    A)   0.39                           

    B)  0.61            

    C)  0.72                            

    D)  0.28

    Correct Answer: A

    Solution :

    [a] \[P\left( A \right)=0.25\] \[P\left( B \right)=0.50\] \[\left( A\cap B \right)=0.14\] \[\therefore P\left( A\cup B \right)=P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\]\[=0.25+0.50-0.14=0.75-0.14=0.61\] Required probability \[=P\left( A\cup B \right)\] \[=1-P\left( A\cup B \right)=1-0.61=0.39\] Hence, option [a] is correct.


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