Volunteer pool of 30: 15M+15F.
Selecting 25 randomly from the pool is limited to the following outcomes:
(1) 15M+10F
(2) 14M+11F
(3) 13M+12F
(4) 12M+13F
(5) 11M+14F
(6) 10M+15F
Out of these 6 possibilities (3) and (4) meet the requirement for 13 males and 12 females, or 12 males and 13 females, the probability is 2/6=1/3.
[(3) gives us 105 ways of selecting 13 males out of 15, and 455 ways of selecting 12 females out of 15. Vice versa for (4).]