- #1

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## Homework Statement

calculate for men and women each, the probability at which...

the lifespan left, of a forty-year-old is 20-40 years.

## Homework Equations

3. The Attempt at a Solution [/B]

That's a mouthful of a sentence.

It looks like if the lifespan is exactly 20 years... there could be many middle-aged men, who live exactly 20 years onwards from exactly 40 years age... Where do those men fit in the table though... There might be men who die exactly on their 60th birthday. What lifespan have they lived? 19.9999 years or 20 years?

Anyways....

It looks like we have to calculate as the base, the forty- year-olds

951 men are alive at exactly 40 years age. We must start from here.

It looks like 20 years afterwards, there are 150 dead male forty-year olds...

- For basic facts it looks like the probability we are interested in, is as follows.

So he lives either 20 years minimum in the future, or maximum of 40 years in the future.

- I suppose the only sensible way to estimate this probability is to look at the number of dead men, between ages 60 - 80. The final two rows. The dead people between ages 40-60 would have contained
*too young dead people*,*who should not have been counted into the 20 year lifespan*. (because many of their lifespans would have been shorter than 20 years required, I think this is the gist of the thing.).

- In other words, if a man dies at the age of 55, he dies between 40-60 years age.
*His lifespan would have been too short to be counted*, because it would have been only 15 years.

- common sense dictates that only those persons who are alive, can later die. So, at the minimum lifespan 20, there are 801 alive. At the maximum lifespan there are 294 alive. Therefore the number of dead men is the difference between.

for men

$$P(man ~~~~lifespan ~~between 20-40)= \frac {801-294} {951}~= 0,5331$$

for women

$$P(~woman ~~~~lifespan ~~between 20-40)= \frac {922-551} {979}= 0,3789$$