After 1-st transfer,


    With the probability   =   you will get (7+1 blue, 3 green) = (8 blue,3 green) in the bag   

    (call it "case A". It is the case when a blue jelly was transferred);



    with the probability   =   you will get (7 blue, 3+1 green) = (7 blue,4 green) in the bag   

    (call it "case B". It is the case when a green jelly was transferred).



After the selection from the bag, 


    the probability to get a green jelly from the bag is   =   in case A,  and

    the probability to get a green jelly from the bag is   =   in case B.



Thus the probability to get a green jelly from the bag is 


    P(green) =  +  =  +   =  = .


Now use the formula for conditional probability to get the answer to the problem's question


    P(green at the first transfer) =  =  =  =  = .    ANSWER