If a person who tests positive in this patient pool takes drug A, he will be killed by side effects 20% of the time and will live the other 80% of the time for a survival rate of 80%.
If he takes drug B, he will live if he either: i) does not have disease in the first place (probability 97.06%); or ii) has disease and is cured (probability 2.94% x 70% = 2.06%). The sum of these cases is 99.12%, which is the survival rate for taking drug B.
Correct of course - and stated more dramatically:
Calculated the correct way the odds of death are more than 20x greater for Drug A than they are for Drug B.
But the human intuitional method can incorrectly get a very very different comparison of the risks of Drug A vs Drug B(as the good sport Tas showed - e.g. about equal odds for drug a and drug b).