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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-5

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

    A) (a) 0.11                        

    B) (b) 0.25           

    C) (c) 0.39                        

    D) (d) 0.45

    Correct Answer: C

    Solution :

    [c] \[\because P\left( A \right)=0.25\] \[P\left( B \right)=0.50\] \[P\left( A\cap B \right)=0.14\] \[P\left( A'\cap B' \right)=P\left( A\cup B \right)'\] \[=1-P\left( A\cup B \right)=1-\left[ P\left( A \right)+P\left( B \right)-P\left( A\cap B \right) \right]\]\[=1-\left( 0.75-0.14 \right)=1-0.61=039.\] Hence, option [c] is correct.


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