question_answer

Events A, B, C are mutually exclusive 3x +1 events   such that \[P(A)=\frac{3x+1}{3},\,P(B)=\frac{1-x}{4}\] and \[P(C)=\frac{1-2x}{2}\]. The set of possible values of x are in the interval     AIEEE  Solved  Paper-2003

A)                         \[\left[ \frac{1}{3},\frac{1}{2} \right]\]   

B) \[\left[ \frac{1}{3},\frac{2}{3} \right]\]                   

C) \[\left[ \frac{1}{3},\frac{13}{3} \right]\]                

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

Correct Answer: A

Solution :

                and                                       ... (i)                                       ... (ii)                                   ?. (iii) and                                                             ?.. (iv) From Eqs. (i), (ii), (iii) and (iv),