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JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    If E and F are events with \[P\,(E)\le P\,(F)\] and \[P\,(E\cap F)>0,\] then                                                       [IIT 1998]

    A)                 Occurrence of \[E\Rightarrow \] Occurrence of F

    B)                 Occurrence of \[F\Rightarrow \]Occurrence of E

    C)                 Non-occurrence of \[E\Rightarrow \] Non-occurrence of F

    D)                 None of the above implications holds

    Correct Answer: D

    Solution :

               \[P(E)\le P(F)\Rightarrow n(E)\le n(F)\]            \[P(E\cap F)>0\Rightarrow E\cap F\ne \varphi \]                 These do not mean that \[E\] is a sub-set of \[F\] or \[F\] is a sub-set of \[E.\] i.e., \[E\subseteq F\] or \[F\subseteq E\] or \[\bar{E}\subseteq \bar{F}\]


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