My mom is in hospital icu with pneumonia and developed ards she as at 90% oxygen and been in induced acoma for 8 days what are her chances of sur?

Case by case: Large studies suggest that overall mortality from ARDS has decreased over the years to just under 30%. But these are just statistics and every patient is different. In general the healthier they were before ards, and the least number of organs other than lungs involved (kidney, heart, blood pressure...) the better the outcome. Hang in there!