Consider a communication system. At any given time, the communication channel is in good condition with probability $0\mathrm{.}8,$ and is in bad condition with probability $0\mathrm{.}2.$ An error occurs in a transmission with probability $0\mathrm{.}1$ if the channel is in good condition, and with probability $0\mathrm{.}3$ if the channel is in bad condition. Let $G$ be the event that the channel is in good condition and $E$ be the event that there is an error in transmission.