A signal which can be green or red with probability $\frac { 4 } { 5 }$ and $\frac { 1 } { 5 }$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac { 3 } { 4 }$. If the signal received at station $B$ is green, then the probability that the original signal was green is\\
A) $\frac { 3 } { 5 }$\\
B) $\frac { 6 } { 7 }$\\
C) $\frac { 20 } { 23 }$\\
D) $\frac { 9 } { 20 }$