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

  • question_answer
    If  \[P\,({{A}_{1}}\cup {{A}_{2}})=1-P(A_{1}^{c})\,P(A_{2}^{c})\] where c stands for complement, then the events \[{{A}_{1}}\] and \[{{A}_{2}}\] are [MP PET 1989]

    A)                 Mutually exclusive

    B)                 Independent

    C)                 Equally likely        

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[P({{A}_{1}}\cup {{A}_{2}})=1-[1-P({{A}_{1}})]\,[1-P({{A}_{2}})]\]                                                       \[=P({{A}_{1}})+P({{A}_{2}})-P({{A}_{1}})\,.\,P({{A}_{2}})\].


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