Sampling and Experiments · Superchallenge problem

In an observational study, doctors chose which patients got a new drug, and they gave it mostly to severe cases. Results: drug, severe: 80 patients, 40 recovered; drug, mild: 20 patients, 18 recovered; no drug, severe: 20 patients, 8 recovered; no drug, mild: 80 patients, 64 recovered. Let $A$ be the drug's overall recovery rate minus the no-drug overall recovery rate, in percentage points. Let $B$ be the same difference expected from a randomized experiment on a population that is half severe and half mild, assuming the recovery rates within each severity level are as above. Find $B - A$.