Events A, B, C are mutually exclusive 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 :

Question

( A ) $[\frac{1}{3}, \frac{2}{3}]$
( B ) $[\frac{1}{3}, \frac{13}{3}]$
( C ) $[\frac{1}{3}, \frac{1}{2}]$
( D ) $[0, 1]$