Probability of dying across multiple periods of time.

Tones · science forum beginner Joined: 26 Sep 2005 Posts: 1

If we know that the probability of dying during any one day is P(?) and we
want to know what is the probability of dying over a period of k days is
this the right way to address this problem

The probability of dying on the first day is P(?).
The probability of dying on the second day is (1- P(?))P(?).
The probability of dying on the third day is (1- P(?)) ^2 P(?).
etc.,
....
....
The probability of dying on any particular day requires that you survive all
preceding ones. Thus this proability is the product of surviving so many
days and then dying on the last.

So, the probability of dying DURING any arbitrary period will be the
probability of dying on the first OR the probability of dying on the second
or the probability of dying on the third, etc., etc., This probability will
be the SUM of the probabilities of dying on ANYof days which are contained
in an arbitrary period of time.

As a result, the probability of dying over a period of T days will be:
P(?) + 1- P(?))P(?) + (1- P(?)) ^2 P(?) + ... ....(1- P(?)) ^T P(?)
which is just a geometric series, that converges since 0 < P(?) < 1. This
also means that the probability of dying at some point across an infinite
future is finite.

I hope I have not buggered this up.

If I have screwed up could someone please tell me where as I would hate to
believe something to be true when it is not.

Thanks
Tones.

Rusty · science forum beginner Joined: 07 Sep 2005 Posts: 46

"Tones" <tones@mayfieldeast.net> wrote in message
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