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?