In reply to tom_in_edinburgh:
> (In reply to Robert Durran)
> Don't you need to know when the one person died to compensate.
> There's also an assumption that the risk of death is constant and doesn't depend on length of exposure.
I am taking the OP to mean that the expected number of deaths among 1000 people over the ten years is 1 (I'm not sure that there is any other sensible interpretation!)
I am then assuming that any given person in any given year (at the start of which they are alive) has the same risk of dying during that year. This is what is being calculated.
Suppose required risk is p.
Then probability that a person does not die in the ten years is (1-p)^10
So probability they do die is 1-(1-p)^10
So expected number of deaths is 1000(1-(1-p)^10)=1
So 1-(1-p)^10=0.001
(1-p)^10=0.999
1-p=0.999^0.1
p=1-0.999^0.1