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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?

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"So, you are looking at the difference between a 99.5 percent chance of staying well, and a 99.5 percent chance of staying well" The second number should be 99.95 (100-0.05). –  InterestedGuest Jan 25 '11 at 17:06
    
O yes. Made the edit. –  user118102114 Jan 26 '11 at 0:44
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up vote 4 down vote accepted

No, they just assumed each day is independent. Without treatment, with 0.5 percent chance per day, the chanceof getting through a year is .995^365=.160 With treatment, you have .9995^365=.833

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