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

  • question_answer
    The probability of happening at least  one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then                                                                               \[P\,(\bar{A})+P\,(\bar{B})=\]                 [Roorkee 1989; IIT 1987; MP PET 1997; DCE 2001; J & K 2005]

    A)                 0.4         

    B)                 0.8

    C)                 1.2

    D)                 1.4

    Correct Answer: C

    Solution :

                       We are given that                                                                                         \[P(A\cup B)=0.6\]  and                                                                                         \[P(A\cap B)=0.2\] .                    We know that if                                                                                                     \[A\]  and                                                                                                     \[B\]  are any two events, then                                                                                                                                                \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                                                                                                                                             \[0.6=1-P(\bar{A})+1-P(\bar{B})-0.2\]                                                                                                                         \[\Rightarrow P(\bar{A})+P(\bar{B})=2-0.8=1.2\].


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