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

  • question_answer
    If \[P(A)=2/3\], \[P(B)=1/2\] and \[\text{ }P(A\cup B)=5/6\] then events A and B are                                 [Kerala (Engg.)  2002]

    A)                 Mutually exclusive

    B)                 Independent as well as mutually exhaustive

    C)                 Independent         

    D)                 Dependent only on A

    Correct Answer: A

    Solution :

                       \[P(A\cup B)=\,P(A)+P(B)-P(A\cap B)\]                     \[\frac{5}{6}=\frac{2}{3}+\frac{1}{2}-P(A\cap B)\] \[\Rightarrow \,P(A\cap \,B)=0\]                 \ Events A and B are mutually exclusive.


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