In a communication system each message (0 or 1) is transmitted three times in order to reduce the probability of error. The detection is based on the majority rule at the receiver. If p_e is the probability of bit error, the probability of error for this communication system is

A. $$3{\text{p}}_{\text{e}}^2 - 2{\text{p}}_{\text{e}}^3$$

B. $$1 - {\text{p}}_{\text{e}}^2 - {\text{p}}_{\text{e}}^3$$

C. $${\text{p}}_{\text{e}}^3$$

D. $${\text{p}}_{\text{e}}^2\left( {1 - {{\text{p}}_{\text{e}}}} \right)$$

Answer: Option A