If you take the “miracle” drug, your chance of surviving is only 64%.
Let's work through the math:
If I do nothing, I have a 20% chance of survival.
If I take the "cure", I have a 0% chance of dying from the original disease, but now I have a 20% of dying from side effects. It doesn't matter whether I was going to die of the original disease or not. My survival percentage is 80%. If I have to break down the math, it goes like this -- the 80% who would have died turn into 64% alive and 16% dead, and the 20% who weren't going to die turn into 16% alive and 4% dead.
If I take the 70% cure drug with no side effects, there are again two groups: (1) the 80% where I was going to die -- 56% now live and 24% still die. In the 20% that weren't going to die anyhow, they all still live due to no side effects. That's 76% vs. 80%.
So even though I thought I was giving the wrong answer (on purpose), I think I gave the right answer. Your 64% math is wrong.
“The trick is in what one emphasizes. We either make ourselves miserable, or we make ourselves happy. The amount of work is the same.” Carlos Castaneda