Consider a binary digital communication system with equally likely $0$'s and $1$'s. When binary 0 is transmitted the voltage at the detector input can lie between the levels $-0.25 \mathrm{~V}$ and $+0.25 \mathrm{~V}$ with equal probability: when binary $1$ is transmitted, the voltage at the detector can have any value between $0$ and $1 \mathrm{~V}$ with equal probability. If the detector has a threshold of $2.0 \mathrm{~V}$ (i.e., if the received signal is greater than $0.2 \mathrm{~V}$, the bit is taken as $1$), the average bit error probability is
- $0.15$
- $0.2$
- $0.05$
- $0.5$