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JEE Main & Advanced JEE Main Paper (Held On 25 April 2013)

  • question_answer
                    If the events A and B are mutually exclusive events such that \[\operatorname{P}(\operatorname{A})=\frac{3x+1}{3}\]\[\operatorname{P}(\operatorname{B})=\frac{1+x}{4},\] then the set of possible values of \[x\] lies in the interval:     JEE Main Online Paper ( Held On 25  April 2013 )

    A)                 \[\left[ 0,1 \right]\]        

    B)                                        \[\left[ \frac{1}{3},\frac{1}{3} \right]\]

    C)                                        \[\left[ -\frac{1}{3},\frac{5}{9} \right]\] 

    D)                                        \[\left[ -\frac{7}{9},\frac{4}{9} \right]\]                

    Correct Answer: C

    Solution :

                     Since events A and Bare mutually exclusive \[\therefore \] P(A)+P(B)=1 \[\Rightarrow \]\[\frac{3x+1}{3}+\frac{1-x}{4}=1\]\[\Rightarrow \]\[12x+4+3-3x=12\] \[\Rightarrow \]\[9x=5\]\[\Rightarrow \]\[x=\frac{5}{9}\] \[\therefore \]\[x\in \left[ -\frac{1}{3},\frac{5}{9} \right]\]


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