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I have a question I don't know how to solve correctly, hope you can help me.

Let's say I have something bad, a cancer or something, and I have each year 1 chance between 750 of dying. The more years I live with the cancer, the more years I am exposed to death.

I want to calculate what chances of dying I have if I live, let's say, 10 years. I know that the more years I live with cancer, the more chances I have to die, but how to calculate them exactly?

I know that is isn't just summing up the chances per year, because if I have a 50% chance of dying, that don't means that in 2 years I'm going to die for sure.

PD: I don't have something bad, is for calculating chances of dying because of smoking, travelling by car, plane, etc...

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  • $\begingroup$ Your chances of dying are 100%. Do you mean to ask about your chances of dying within a certain timeframe? Also, I just wanted to point out that, the way you've phrased the question, the condition doesn't "get worse" - the chance of dying in any given year is exactly $1/750$, always. $\endgroup$ – Zev Chonoles Jun 8 '13 at 13:26
  • $\begingroup$ Yes, the chances of dying within a certain timeframe if I have a chance of dying of 50% each year. $\endgroup$ – Jorge Fuentes González Jun 8 '13 at 13:27
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Assuming independence of the "death lottery" over the years, the probability of surviving $n$ consecutive years is $(1-p)^n$, hence the risk of dying is $1-(1-p)^n$. For example with two years and a 50% death probability, that is $p=0.5$ and $n=2$, you get $0.75$ as death probability instead of $1$.

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  • $\begingroup$ Perfect, that's what I needed. Thank you! (I have to wait 9 minutes to accept the answer) $\endgroup$ – Jorge Fuentes González Jun 8 '13 at 13:28

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