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JEE Main & Advanced Mathematics Probability Question Bank Definition of various terms

  • question_answer
    If A and B are two independent events, then A and \[\bar{B}\] are

    A)                 Not independent  

    B)                 Also independent

    C)                 Mutually exclusive

    D)                 None of these

    Correct Answer: B

    Solution :

                       Since \[A\cap \bar{B}\] and \[A\cap B\] are mutually exclusive events such that \[A=(A\cap \bar{B})\cup (A\cap B)\]            \ \[P(A)=P(A\cap \bar{B})+P(A\cap B)\]            \[\Rightarrow P(A\cap \bar{B})=P(A)-P(A\cap B)\]\[=P(A)-P(A)P(B)\]   \[(\because \,\,\,A,\,B\] are independent)            \[\Rightarrow P(A\cap \bar{B})\]\[=P(A)(1-P(B))=P(A)P(\bar{B})\]                 \[\therefore \,\,\,A\] and \[\bar{B}\] are also independent.


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