Probability

Let $B(\alpha, \beta, \gamma)$ represents that a bag $B$ contains $\alpha$ red balls, $\beta$ green balls and $\gamma$ blue balls. Given $B_1(2,3,2), B_2(3,2,2), B_3(2,2,3)$. A die is rolled. If the die shows up 2 or 3 or 5 , then a ball will be drawn at random from bag $B_1$. If the die shows up 4 or 6 , then a ball will be drawn at random from bag $B_2$. If the die shows up 1 , then from bag $B_3$ a ball will be drawn at random. Then the probability of drawing a green ball from a bag thus chosen is