Group 1: 4B+2G (6 students); Group 2: 3B+1G (4 students).
There are 4 ways of selecting students:
(A) bb (B) bg (C) gb (D) gg and the associated probabilities are:
(A) 2/3*3/4=1/2 (B) 2/3*1/4=1/6 (C) 1/3*3/4=1/4 (D) 1/3*1/4=1/12.
These probabilities add up to 1. We need (B)+(C)=5/12.