Bag1(B1) - {3R, 7G}
Bag2(B2) - {4R, 8G}
P(Choosing B1) = 1/2 (if Head)
P(Choosing B2) = 1/2 (if Tail)
P(B1/R) = $\frac{P(B1) * P(R/B1)}{P(B1) * P(R/B1) + P(B2) * P(R/B2)}$
$\frac{1/2 * 3/10 * 2/1}{(1/2 * 3/10 * 2/1) + (1/2 * 4/12 * 2/1)}$ = 6/11
Point out my mistakes, if any !!