A source emits bit 0 with probability $$\frac{1}{3}$$ and bit 1 with probability $$\frac{2}{3}.$$ The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R as
\[\begin{array}{l} {f_{R/0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \le r \le 1}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right.\,{\rm{and}}\\ {f_{R/1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \le r \le 5}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right. \end{array}\]
The minimum decision error probability is

A. $$0$$

B. $$\frac{1}{{12}}$$

C. $$\frac{1}{9}$$

D. $$\frac{1}{6}$$

Answer: Option D