I was reading this book about medicine and I found this paragraph in it
A person's daily risk of getting lung illness ... is $0.5$ percent. The daily risk of getting a bad lung illness ... plus treatment is $0.05$ percent. So, you are looking at the difference between a $99.5$ percent chance of staying well, and a $99.95$ percent chance of staying well ... But sum it up over a year and it is the difference between an $83$ percent chance of making it through the year healthy, and a $16$ percent chance.
I don't understand how this conclusion was reached. Was some additional data assumed?