Is the chance of surviving stage 3 lung cancer usually slim?

It depends. The overall 5-year survival rate with stage 3a lung cancer is 23%, but it can vary widely. The 5-year survival rate with stage 3b lung cancer is sadly only about 10%.
Statistics. Studies report very concrete numbers based on the individuals entered, and how well they fared with a "standard" treatment or a newly tested, or experimental treatment. They are tools to establish benchmarks, but they never tell what will happen to an individual (cohort vs person). One can say the chances of 5 year survival are about 30% today, but some individuals die in a few weeks to months.