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JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    If                                                                  \[P\,(A)=0.4,\,\,P\,(B)=x,\,\,P\,(A\cup B)=0.7\] and the events A and B are mutually exclusive, then                                                                                                    \[x=\]                 [MP PET 1992]

    A)                                                                                            \[\frac{3}{10}\]                                                                                          

    B)                                                                                             \[\frac{1}{2}\]

    C)                                                                                             \[\frac{2}{5}\]                                                                                           

    D)                                                                                             \[\frac{1}{5}\]

    Correct Answer: A

    Solution :

                       Since events are mutually exclusive, therefore                                                                                                                  \[P(AB)=0\]  i.e.,                                                                                  \[P(A\cup B)=P(A)+P(B)\]                                                                                                                  \[\Rightarrow 0.7=0.4+x\Rightarrow x=\frac{3}{10}.\]


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