You're off by a factor of 10 on your percentage calculations. With a 99.8% recovery rate, your risk of dying is 0.2%, or 0.002. Without the vaccine, you would die 2 times out of 1000. If the vaccine is 90% effective, then by your calculation you would die 0.2 times out of 1000.
Another way to say it is, the vaccine supposedly increases your recovery rate from 99.80% to 99.98%
You're off by a factor of 10 on your percentage calculations. With a 99.8% recovery rate, your risk of dying is 0.2%, or 0.002. Without the vaccine, you would die 2 times out of 1000. If the vaccine is 90% effective, then by your calculation you would die 0.2 times out of 1000.
Another way to say it is, the vaccine supposedly increases your recovery rate from 99.80% to 99.98%