What are the chances of lung collapse during a biopsy?

Depends: The risk of pneumothorax (collapsed lung) depends on the type of procedure. If you are underoing a bronchoscopy (camera/scope of the lung) the risk is about 1 in 500; if you are having a ct guided needle biopsy by a radiologist the risk is somewhat lower but it really depends on the location of the abnormality in the chest. (if it is near the edge of the lung the risk is very low).

CT is higher: The risk from a ct guided lung biopsy is approximately 25%. Underlying emphysema would make a collapsed lung more likely. Biopsy of a mass resting against the chest wall would be less likely to cause collapse. I am not sure about the discrepancy between the two answers. I do ct guided lung biopsies all the time, and have the same collapse rates as other docs in my group.

May be even higher: Ct biopsies are becoming more invasive. Core biopsies are favored and more passes are being made to allow special staining and even chemotherapy resistance evaluation of cancer stem cells. This can lead to rates as high as 50%.