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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 that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then \[P({A}')+P({B}')\] is [DCE 2002]

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

    B)                 \[\frac{4}{5}\]

    C)                 \[\frac{6}{5}\]       

    D)                 \[\frac{7}{5}\]

    Correct Answer: C

    Solution :

                       Given \[P(A\cup B)=\frac{3}{5}\] and \[P(A\cap B)=\frac{1}{5}\]                    We know \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                    \[\frac{3}{5}=1-P(\overline{A})+1-P(\overline{B})-\frac{1}{5}\]                                 \[2-\frac{4}{5}=P(\overline{A})+P(\overline{B})\]\[\Rightarrow \]\[P(\overline{A})+P(\overline{B})=\frac{6}{5}\].


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