The probability of choosing two green balls without replacement is 1150 , and the probability of choosing one green ball is1225 .

12/25  (     )   =  11/50

(     )   =    11/50 * 25/12    =   275 / 600   =   

11/24

This can also be found by "formula"

Let A  =  Prob of second ball green

B  = First ball is green  =  12/25

P (A and B)  =  P (Both balls are green)  =  11/50

P ( A  given B )   =   P( A and B)  / P (B) 

So we have  :

P ( A given B)  =   ( 11/50) / (12/25)   =   (11/50) (25/12)  =  11/24