Check your math. If you are Resistance and not on the mission, then there are 3 other resistance members and two spies. For the mission to succeed, 2 people must be picked, and both must be resistance. The first is chosen with a 3/5 chance of being good, and the second has a 2/4 chance of being good, so the actual odds are 6/20 = 30%. (Alternatively, you can calculate this as (3 choose 2)/(5 choose 2), which gives the same result.)
*Sigh* I even have to do the math for the mathematician here. We are surely doomed.