Alice has two urns A and B each containing four indistinguishable balls.\\
Urn A contains two green balls and two red balls.\\
Urn B contains three green balls and one red ball.\\
Alice randomly chooses an urn and then a ball from that urn. She obtains a green ball.\\
The probability that she chose urn B is:\\
A. $\frac{3}{8}$\\
B. $\frac{1}{2}$\\
C. $\frac{3}{5}$\\
D. $\frac{5}{8}$